The goal of this exercice is to decipher relevant knowledge from Basket DataSet.

Summarise basket object

# get the structure of the dataset
str(basket)
## 'data.frame':    38765 obs. of  3 variables:
##  $ Member_number  : int  1808 2552 2300 1187 3037 4941 4501 3803 2762 4119 ...
##  $ Date           : Factor w/ 728 levels "01-01-2014","01-01-2015",..: 494 98 450 288 4 316 178 552 462 268 ...
##  $ itemDescription: Factor w/ 167 levels "abrasive cleaner",..: 156 165 109 102 165 122 102 112 165 156 ...
summary(basket)
##  Member_number          Date               itemDescription 
##  Min.   :1000   21-01-2015:   96   whole milk      : 2502  
##  1st Qu.:2002   21-07-2015:   93   other vegetables: 1898  
##  Median :3005   08-08-2015:   92   rolls/buns      : 1716  
##  Mean   :3004   29-11-2015:   92   soda            : 1514  
##  3rd Qu.:4007   30-04-2015:   91   yogurt          : 1334  
##  Max.   :5000   26-03-2015:   88   root vegetables : 1071  
##                 (Other)   :38213   (Other)         :28730

The dataset is a dataframe with 3 columns: Member_number, Date, and Products description. The Member_number column must be considered as factor, like the id of member. The Date must be a date type. The itemDascription is already as.factor

convert the type of variables

library(magrittr)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
basket$Member_number <- as.factor(basket$Member_number)
basket$Date <- as.Date(basket$Date, "%d-%m-%Y")
# review the structure and summary
str(basket)
## 'data.frame':    38765 obs. of  3 variables:
##  $ Member_number  : Factor w/ 3898 levels "1000","1001",..: 787 1505 1264 181 1982 3839 3407 2732 1712 3037 ...
##  $ Date           : Date, format: "2015-07-21" "2015-01-05" ...
##  $ itemDescription: Factor w/ 167 levels "abrasive cleaner",..: 156 165 109 102 165 122 102 112 165 156 ...
summary(basket)
##  Member_number        Date                    itemDescription 
##  3180   :   36   Min.   :2014-01-01   whole milk      : 2502  
##  2051   :   33   1st Qu.:2014-07-12   other vegetables: 1898  
##  3050   :   33   Median :2015-01-21   rolls/buns      : 1716  
##  3737   :   33   Mean   :2015-01-09   soda            : 1514  
##  2271   :   31   3rd Qu.:2015-07-10   yogurt          : 1334  
##  2433   :   31   Max.   :2015-12-30   root vegetables : 1071  
##  (Other):38568                        (Other)         :28730

Now is better formated. We can observe: + The Member 3180 has the biggest operations (36). + The Whole milk product is the most sold with 2502 operations. + The sampling data was done during two years, between 2014-01-01 and 2015-12-30.

Before to start the exploration, It is important to check if the dataset countain empty cells or non available data.

check for any empty or NA cell

# Ckeck for Non Available (NA) cell
all(is.na(basket))
## [1] FALSE

There is an intersting package named funModeling that make eeasy the exploration of Data analysis. We will use it.

library(funModeling) 
## Loading required package: Hmisc
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
## Loading required package: ggplot2
## 
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:dplyr':
## 
##     src, summarize
## The following objects are masked from 'package:base':
## 
##     format.pval, units
## funModeling v.1.6.8 :)
## Examples and tutorials at livebook.datascienceheroes.com
library(tidyverse) 
## ── Attaching packages ────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
## ✔ tibble  1.4.2     ✔ purrr   0.2.5
## ✔ tidyr   0.8.2     ✔ stringr 1.3.1
## ✔ readr   1.2.1     ✔ forcats 0.3.0
## ── Conflicts ───────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ tidyr::extract()   masks magrittr::extract()
## ✖ dplyr::filter()    masks stats::filter()
## ✖ dplyr::lag()       masks stats::lag()
## ✖ purrr::set_names() masks magrittr::set_names()
## ✖ Hmisc::src()       masks dplyr::src()
## ✖ Hmisc::summarize() masks dplyr::summarize()
library(Hmisc)

tibble::glimpse(basket)
## Observations: 38,765
## Variables: 3
## $ Member_number   <fct> 1808, 2552, 2300, 1187, 3037, 4941, 4501, 3803...
## $ Date            <date> 2015-07-21, 2015-01-05, 2015-09-19, 2015-12-1...
## $ itemDescription <fct> tropical fruit, whole milk, pip fruit, other v...

glimpse function returns informations like str.

 funModeling::df_status(basket)
##          variable q_zeros p_zeros q_na p_na q_inf p_inf   type unique
## 1   Member_number       0       0    0    0     0     0 factor   3898
## 2            Date       0       0    0    0     0     0   Date    728
## 3 itemDescription       0       0    0    0     0     0 factor    167

df_statut allows us to detect abnormal values and if is there non available or empty cells.

 freq(basket) 
## Warning in freq_logic(data = data, input = input[i], plot, na.rm, path_out
## = path_out): Skipping plot for variable 'Member_number' (more than 100
## categories)
##      Member_number frequency percentage cumulative_perc
## 1             3180        36       0.09            0.09
## 2             2051        33       0.09            0.18
## 3             3050        33       0.09            0.27
## 4             3737        33       0.09            0.36
## 5             2271        31       0.08            0.44
## 6             2433        31       0.08            0.52
## 7             2625        31       0.08            0.60
## 8             3915        31       0.08            0.68
## 9             3872        30       0.08            0.76
## 10            2394        29       0.07            0.83
## 11            2851        29       0.07            0.90
## 12            3289        29       0.07            0.97
## 13            4875        29       0.07            1.04
## 14            1379        28       0.07            1.11
## 15            2524        28       0.07            1.18
## 16            3308        28       0.07            1.25
## 17            4338        28       0.07            1.32
## 18            4831        28       0.07            1.39
## 19            1052        27       0.07            1.46
## 20            1410        27       0.07            1.53
## 21            1998        27       0.07            1.60
## 22            2193        27       0.07            1.67
## 23            2517        27       0.07            1.74
## 24            2663        27       0.07            1.81
## 25            3752        27       0.07            1.88
## 26            4272        27       0.07            1.95
## 27            1905        26       0.07            2.02
## 28            2512        26       0.07            2.09
## 29            2960        26       0.07            2.16
## 30            3082        26       0.07            2.23
## 31            4137        26       0.07            2.30
## 32            4376        26       0.07            2.37
## 33            4486        26       0.07            2.44
## 34            4695        26       0.07            2.51
## 35            4941        26       0.07            2.58
## 36            1265        25       0.06            2.64
## 37            1366        25       0.06            2.70
## 38            1793        25       0.06            2.76
## 39            1870        25       0.06            2.82
## 40            2164        25       0.06            2.88
## 41            2344        25       0.06            2.94
## 42            2440        25       0.06            3.00
## 43            3462        25       0.06            3.06
## 44            4217        25       0.06            3.12
## 45            4303        25       0.06            3.18
## 46            4864        25       0.06            3.24
## 47            1098        24       0.06            3.30
## 48            1116        24       0.06            3.36
## 49            1275        24       0.06            3.42
## 50            2070        24       0.06            3.48
## 51            2184        24       0.06            3.54
## 52            2560        24       0.06            3.60
## 53            2632        24       0.06            3.66
## 54            2816        24       0.06            3.72
## 55            2990        24       0.06            3.78
## 56            3120        24       0.06            3.84
## 57            3122        24       0.06            3.90
## 58            3247        24       0.06            3.96
## 59            3957        24       0.06            4.02
## 60            4828        24       0.06            4.08
## 61            1395        23       0.06            4.14
## 62            1407        23       0.06            4.20
## 63            1466        23       0.06            4.26
## 64            1574        23       0.06            4.32
## 65            1654        23       0.06            4.38
## 66            1827        23       0.06            4.44
## 67            1991        23       0.06            4.50
## 68            2022        23       0.06            4.56
## 69            2294        23       0.06            4.62
## 70            2706        23       0.06            4.68
## 71            2736        23       0.06            4.74
## 72            2760        23       0.06            4.80
## 73            2789        23       0.06            4.86
## 74            2855        23       0.06            4.92
## 75            3046        23       0.06            4.98
## 76            3221        23       0.06            5.04
## 77            3484        23       0.06            5.10
## 78            3497        23       0.06            5.16
## 79            3593        23       0.06            5.22
## 80            3691        23       0.06            5.28
## 81            3783        23       0.06            5.34
## 82            3830        23       0.06            5.40
## 83            3942        23       0.06            5.46
## 84            3960        23       0.06            5.52
## 85            4277        23       0.06            5.58
## 86            4297        23       0.06            5.64
## 87            4437        23       0.06            5.70
## 88            4495        23       0.06            5.76
## 89            4753        23       0.06            5.82
## 90            1595        22       0.06            5.88
## 91            1887        22       0.06            5.94
## 92            1948        22       0.06            6.00
## 93            2229        22       0.06            6.06
## 94            2270        22       0.06            6.12
## 95            2779        22       0.06            6.18
## 96            3042        22       0.06            6.24
## 97            3090        22       0.06            6.30
## 98            3246        22       0.06            6.36
## 99            3266        22       0.06            6.42
## 100           3361        22       0.06            6.48
## 101           3465        22       0.06            6.54
## 102           3495        22       0.06            6.60
## 103           3517        22       0.06            6.66
## 104           3543        22       0.06            6.72
## 105           4153        22       0.06            6.78
## 106           4251        22       0.06            6.84
## 107           4293        22       0.06            6.90
## 108           4364        22       0.06            6.96
## 109           4524        22       0.06            7.02
## 110           4624        22       0.06            7.08
## 111           4671        22       0.06            7.14
## 112           4679        22       0.06            7.20
## 113           1004        21       0.05            7.25
## 114           1087        21       0.05            7.30
## 115           1169        21       0.05            7.35
## 116           1218        21       0.05            7.40
## 117           1225        21       0.05            7.45
## 118           1353        21       0.05            7.50
## 119           1566        21       0.05            7.55
## 120           1583        21       0.05            7.60
## 121           1737        21       0.05            7.65
## 122           1780        21       0.05            7.70
## 123           1878        21       0.05            7.75
## 124           1929        21       0.05            7.80
## 125           1997        21       0.05            7.85
## 126           2234        21       0.05            7.90
## 127           2252        21       0.05            7.95
## 128           2408        21       0.05            8.00
## 129           2421        21       0.05            8.05
## 130           2443        21       0.05            8.10
## 131           2447        21       0.05            8.15
## 132           2492        21       0.05            8.20
## 133           2511        21       0.05            8.25
## 134           2738        21       0.05            8.30
## 135           2799        21       0.05            8.35
## 136           2868        21       0.05            8.40
## 137           2918        21       0.05            8.45
## 138           3164        21       0.05            8.50
## 139           3248        21       0.05            8.55
## 140           3251        21       0.05            8.60
## 141           3402        21       0.05            8.65
## 142           3635        21       0.05            8.70
## 143           3651        21       0.05            8.75
## 144           3679        21       0.05            8.80
## 145           3709        21       0.05            8.85
## 146           3732        21       0.05            8.90
## 147           3761        21       0.05            8.95
## 148           3811        21       0.05            9.00
## 149           3835        21       0.05            9.05
## 150           3862        21       0.05            9.10
## 151           4187        21       0.05            9.15
## 152           4190        21       0.05            9.20
## 153           4494        21       0.05            9.25
## 154           4574        21       0.05            9.30
## 155           4585        21       0.05            9.35
## 156           4588        21       0.05            9.40
## 157           4656        21       0.05            9.45
## 158           4683        21       0.05            9.50
## 159           4783        21       0.05            9.55
## 160           4877        21       0.05            9.60
## 161           4933        21       0.05            9.65
## 162           1051        20       0.05            9.70
## 163           1092        20       0.05            9.75
## 164           1094        20       0.05            9.80
## 165           1107        20       0.05            9.85
## 166           1146        20       0.05            9.90
## 167           1170        20       0.05            9.95
## 168           1237        20       0.05           10.00
## 169           1245        20       0.05           10.05
## 170           1444        20       0.05           10.10
## 171           1482        20       0.05           10.15
## 172           1483        20       0.05           10.20
## 173           1561        20       0.05           10.25
## 174           1572        20       0.05           10.30
## 175           1682        20       0.05           10.35
## 176           1768        20       0.05           10.40
## 177           1777        20       0.05           10.45
## 178           1785        20       0.05           10.50
## 179           1908        20       0.05           10.55
## 180           1932        20       0.05           10.60
## 181           1943        20       0.05           10.65
## 182           2001        20       0.05           10.70
## 183           2086        20       0.05           10.75
## 184           2186        20       0.05           10.80
## 185           2298        20       0.05           10.85
## 186           2357        20       0.05           10.90
## 187           2454        20       0.05           10.95
## 188           2584        20       0.05           11.00
## 189           2718        20       0.05           11.05
## 190           2758        20       0.05           11.10
## 191           2811        20       0.05           11.15
## 192           2961        20       0.05           11.20
## 193           3393        20       0.05           11.25
## 194           3549        20       0.05           11.30
## 195           3581        20       0.05           11.35
## 196           3657        20       0.05           11.40
## 197           3812        20       0.05           11.45
## 198           4030        20       0.05           11.50
## 199           4165        20       0.05           11.55
## 200           4178        20       0.05           11.60
## 201           4234        20       0.05           11.65
## 202           4292        20       0.05           11.70
## 203           4302        20       0.05           11.75
## 204           4316        20       0.05           11.80
## 205           4509        20       0.05           11.85
## 206           4526        20       0.05           11.90
## 207           4628        20       0.05           11.95
## 208           4645        20       0.05           12.00
## 209           4657        20       0.05           12.05
## 210           4666        20       0.05           12.10
## 211           4694        20       0.05           12.15
## 212           4780        20       0.05           12.20
## 213           4852        20       0.05           12.25
## 214           1013        19       0.05           12.30
## 215           1038        19       0.05           12.35
## 216           1136        19       0.05           12.40
## 217           1148        19       0.05           12.45
## 218           1175        19       0.05           12.50
## 219           1233        19       0.05           12.55
## 220           1235        19       0.05           12.60
## 221           1422        19       0.05           12.65
## 222           1522        19       0.05           12.70
## 223           1565        19       0.05           12.75
## 224           1634        19       0.05           12.80
## 225           1711        19       0.05           12.85
## 226           1748        19       0.05           12.90
## 227           1922        19       0.05           12.95
## 228           1934        19       0.05           13.00
## 229           1959        19       0.05           13.05
## 230           2014        19       0.05           13.10
## 231           2107        19       0.05           13.15
## 232           2142        19       0.05           13.20
## 233           2210        19       0.05           13.25
## 234           2222        19       0.05           13.30
## 235           2293        19       0.05           13.35
## 236           2370        19       0.05           13.40
## 237           2381        19       0.05           13.45
## 238           2568        19       0.05           13.50
## 239           2589        19       0.05           13.55
## 240           2600        19       0.05           13.60
## 241           2601        19       0.05           13.65
## 242           2629        19       0.05           13.70
## 243           2645        19       0.05           13.75
## 244           2654        19       0.05           13.80
## 245           2694        19       0.05           13.85
## 246           2835        19       0.05           13.90
## 247           2957        19       0.05           13.95
## 248           2978        19       0.05           14.00
## 249           3044        19       0.05           14.05
## 250           3048        19       0.05           14.10
## 251           3137        19       0.05           14.15
## 252           3353        19       0.05           14.20
## 253           3504        19       0.05           14.25
## 254           3547        19       0.05           14.30
## 255           3582        19       0.05           14.35
## 256           3663        19       0.05           14.40
## 257           3682        19       0.05           14.45
## 258           3687        19       0.05           14.50
## 259           3719        19       0.05           14.55
## 260           3803        19       0.05           14.60
## 261           3822        19       0.05           14.65
## 262           3903        19       0.05           14.70
## 263           4102        19       0.05           14.75
## 264           4235        19       0.05           14.80
## 265           4266        19       0.05           14.85
## 266           4308        19       0.05           14.90
## 267           4487        19       0.05           14.95
## 268           4515        19       0.05           15.00
## 269           4721        19       0.05           15.05
## 270           4799        19       0.05           15.10
## 271           4836        19       0.05           15.15
## 272           1110        18       0.05           15.20
## 273           1118        18       0.05           15.25
## 274           1197        18       0.05           15.30
## 275           1327        18       0.05           15.35
## 276           1333        18       0.05           15.40
## 277           1404        18       0.05           15.45
## 278           1456        18       0.05           15.50
## 279           1509        18       0.05           15.55
## 280           1510        18       0.05           15.60
## 281           1534        18       0.05           15.65
## 282           1608        18       0.05           15.70
## 283           1625        18       0.05           15.75
## 284           1649        18       0.05           15.80
## 285           1653        18       0.05           15.85
## 286           1761        18       0.05           15.90
## 287           1783        18       0.05           15.95
## 288           1811        18       0.05           16.00
## 289           1866        18       0.05           16.05
## 290           1889        18       0.05           16.10
## 291           2011        18       0.05           16.15
## 292           2019        18       0.05           16.20
## 293           2056        18       0.05           16.25
## 294           2138        18       0.05           16.30
## 295           2171        18       0.05           16.35
## 296           2230        18       0.05           16.40
## 297           2311        18       0.05           16.45
## 298           2340        18       0.05           16.50
## 299           2348        18       0.05           16.55
## 300           2578        18       0.05           16.60
## 301           2612        18       0.05           16.65
## 302           2729        18       0.05           16.70
## 303           2794        18       0.05           16.75
## 304           2946        18       0.05           16.80
## 305           3054        18       0.05           16.85
## 306           3104        18       0.05           16.90
## 307           3165        18       0.05           16.95
## 308           3225        18       0.05           17.00
## 309           3245        18       0.05           17.05
## 310           3358        18       0.05           17.10
## 311           3380        18       0.05           17.15
## 312           3405        18       0.05           17.20
## 313           3429        18       0.05           17.25
## 314           3499        18       0.05           17.30
## 315           3507        18       0.05           17.35
## 316           3562        18       0.05           17.40
## 317           3621        18       0.05           17.45
## 318           3718        18       0.05           17.50
## 319           3757        18       0.05           17.55
## 320           3782        18       0.05           17.60
## 321           3793        18       0.05           17.65
## 322           3855        18       0.05           17.70
## 323           3879        18       0.05           17.75
## 324           3922        18       0.05           17.80
## 325           3926        18       0.05           17.85
## 326           4112        18       0.05           17.90
## 327           4215        18       0.05           17.95
## 328           4321        18       0.05           18.00
## 329           4330        18       0.05           18.05
## 330           4453        18       0.05           18.10
## 331           4572        18       0.05           18.15
## 332           4594        18       0.05           18.20
## 333           4598        18       0.05           18.25
## 334           4693        18       0.05           18.30
## 335           4699        18       0.05           18.35
## 336           4760        18       0.05           18.40
## 337           4773        18       0.05           18.45
## 338           4820        18       0.05           18.50
## 339           4946        18       0.05           18.55
## 340           4988        18       0.05           18.60
## 341           1023        17       0.04           18.64
## 342           1026        17       0.04           18.68
## 343           1097        17       0.04           18.72
## 344           1120        17       0.04           18.76
## 345           1153        17       0.04           18.80
## 346           1190        17       0.04           18.84
## 347           1220        17       0.04           18.88
## 348           1242        17       0.04           18.92
## 349           1264        17       0.04           18.96
## 350           1279        17       0.04           19.00
## 351           1283        17       0.04           19.04
## 352           1287        17       0.04           19.08
## 353           1296        17       0.04           19.12
## 354           1361        17       0.04           19.16
## 355           1438        17       0.04           19.20
## 356           1465        17       0.04           19.24
## 357           1477        17       0.04           19.28
## 358           1486        17       0.04           19.32
## 359           1567        17       0.04           19.36
## 360           1646        17       0.04           19.40
## 361           1661        17       0.04           19.44
## 362           1715        17       0.04           19.48
## 363           1733        17       0.04           19.52
## 364           1734        17       0.04           19.56
## 365           1753        17       0.04           19.60
## 366           1798        17       0.04           19.64
## 367           1819        17       0.04           19.68
## 368           1979        17       0.04           19.72
## 369           1995        17       0.04           19.76
## 370           2055        17       0.04           19.80
## 371           2092        17       0.04           19.84
## 372           2365        17       0.04           19.88
## 373           2406        17       0.04           19.92
## 374           2426        17       0.04           19.96
## 375           2428        17       0.04           20.00
## 376           2448        17       0.04           20.04
## 377           2494        17       0.04           20.08
## 378           2540        17       0.04           20.12
## 379           2595        17       0.04           20.16
## 380           2602        17       0.04           20.20
## 381           2613        17       0.04           20.24
## 382           2690        17       0.04           20.28
## 383           2707        17       0.04           20.32
## 384           2743        17       0.04           20.36
## 385           2810        17       0.04           20.40
## 386           2814        17       0.04           20.44
## 387           2907        17       0.04           20.48
## 388           2932        17       0.04           20.52
## 389           2937        17       0.04           20.56
## 390           2986        17       0.04           20.60
## 391           3002        17       0.04           20.64
## 392           3014        17       0.04           20.68
## 393           3036        17       0.04           20.72
## 394           3072        17       0.04           20.76
## 395           3077        17       0.04           20.80
## 396           3094        17       0.04           20.84
## 397           3119        17       0.04           20.88
## 398           3128        17       0.04           20.92
## 399           3141        17       0.04           20.96
## 400           3189        17       0.04           21.00
## 401           3201        17       0.04           21.04
## 402           3255        17       0.04           21.08
## 403           3450        17       0.04           21.12
## 404           3500        17       0.04           21.16
## 405           3508        17       0.04           21.20
## 406           3531        17       0.04           21.24
## 407           3558        17       0.04           21.28
## 408           3560        17       0.04           21.32
## 409           3595        17       0.04           21.36
## 410           3649        17       0.04           21.40
## 411           3743        17       0.04           21.44
## 412           3776        17       0.04           21.48
## 413           3821        17       0.04           21.52
## 414           3827        17       0.04           21.56
## 415           3841        17       0.04           21.60
## 416           3998        17       0.04           21.64
## 417           4015        17       0.04           21.68
## 418           4018        17       0.04           21.72
## 419           4019        17       0.04           21.76
## 420           4124        17       0.04           21.80
## 421           4129        17       0.04           21.84
## 422           4155        17       0.04           21.88
## 423           4183        17       0.04           21.92
## 424           4197        17       0.04           21.96
## 425           4223        17       0.04           22.00
## 426           4262        17       0.04           22.04
## 427           4312        17       0.04           22.08
## 428           4314        17       0.04           22.12
## 429           4335        17       0.04           22.16
## 430           4353        17       0.04           22.20
## 431           4387        17       0.04           22.24
## 432           4389        17       0.04           22.28
## 433           4406        17       0.04           22.32
## 434           4433        17       0.04           22.36
## 435           4456        17       0.04           22.40
## 436           4464        17       0.04           22.44
## 437           4468        17       0.04           22.48
## 438           4510        17       0.04           22.52
## 439           4531        17       0.04           22.56
## 440           4564        17       0.04           22.60
## 441           4636        17       0.04           22.64
## 442           4661        17       0.04           22.68
## 443           4667        17       0.04           22.72
## 444           4741        17       0.04           22.76
## 445           4745        17       0.04           22.80
## 446           4766        17       0.04           22.84
## 447           4776        17       0.04           22.88
## 448           4804        17       0.04           22.92
## 449           4939        17       0.04           22.96
## 450           1032        16       0.04           23.00
## 451           1062        16       0.04           23.04
## 452           1081        16       0.04           23.08
## 453           1114        16       0.04           23.12
## 454           1144        16       0.04           23.16
## 455           1182        16       0.04           23.20
## 456           1183        16       0.04           23.24
## 457           1204        16       0.04           23.28
## 458           1211        16       0.04           23.32
## 459           1231        16       0.04           23.36
## 460           1239        16       0.04           23.40
## 461           1248        16       0.04           23.44
## 462           1286        16       0.04           23.48
## 463           1329        16       0.04           23.52
## 464           1360        16       0.04           23.56
## 465           1427        16       0.04           23.60
## 466           1430        16       0.04           23.64
## 467           1450        16       0.04           23.68
## 468           1472        16       0.04           23.72
## 469           1494        16       0.04           23.76
## 470           1500        16       0.04           23.80
## 471           1507        16       0.04           23.84
## 472           1580        16       0.04           23.88
## 473           1584        16       0.04           23.92
## 474           1612        16       0.04           23.96
## 475           1618        16       0.04           24.00
## 476           1651        16       0.04           24.04
## 477           1690        16       0.04           24.08
## 478           1708        16       0.04           24.12
## 479           1740        16       0.04           24.16
## 480           1788        16       0.04           24.20
## 481           1832        16       0.04           24.24
## 482           1913        16       0.04           24.28
## 483           1931        16       0.04           24.32
## 484           1966        16       0.04           24.36
## 485           1983        16       0.04           24.40
## 486           1999        16       0.04           24.44
## 487           2017        16       0.04           24.48
## 488           2043        16       0.04           24.52
## 489           2089        16       0.04           24.56
## 490           2093        16       0.04           24.60
## 491           2129        16       0.04           24.64
## 492           2133        16       0.04           24.68
## 493           2251        16       0.04           24.72
## 494           2289        16       0.04           24.76
## 495           2310        16       0.04           24.80
## 496           2349        16       0.04           24.84
## 497           2380        16       0.04           24.88
## 498           2389        16       0.04           24.92
## 499           2549        16       0.04           24.96
## 500           2550        16       0.04           25.00
## 501           2555        16       0.04           25.04
## 502           2573        16       0.04           25.08
## 503           2592        16       0.04           25.12
## 504           2617        16       0.04           25.16
## 505           2618        16       0.04           25.20
## 506           2633        16       0.04           25.24
## 507           2650        16       0.04           25.28
## 508           2659        16       0.04           25.32
## 509           2666        16       0.04           25.36
## 510           2687        16       0.04           25.40
## 511           2716        16       0.04           25.44
## 512           2772        16       0.04           25.48
## 513           2787        16       0.04           25.52
## 514           2813        16       0.04           25.56
## 515           2873        16       0.04           25.60
## 516           2874        16       0.04           25.64
## 517           2925        16       0.04           25.68
## 518           2997        16       0.04           25.72
## 519           3095        16       0.04           25.76
## 520           3111        16       0.04           25.80
## 521           3115        16       0.04           25.84
## 522           3139        16       0.04           25.88
## 523           3153        16       0.04           25.92
## 524           3232        16       0.04           25.96
## 525           3262        16       0.04           26.00
## 526           3268        16       0.04           26.04
## 527           3284        16       0.04           26.08
## 528           3306        16       0.04           26.12
## 529           3309        16       0.04           26.16
## 530           3322        16       0.04           26.20
## 531           3337        16       0.04           26.24
## 532           3356        16       0.04           26.28
## 533           3430        16       0.04           26.32
## 534           3438        16       0.04           26.36
## 535           3460        16       0.04           26.40
## 536           3469        16       0.04           26.44
## 537           3474        16       0.04           26.48
## 538           3481        16       0.04           26.52
## 539           3518        16       0.04           26.56
## 540           3523        16       0.04           26.60
## 541           3633        16       0.04           26.64
## 542           3741        16       0.04           26.68
## 543           3768        16       0.04           26.72
## 544           3844        16       0.04           26.76
## 545           3877        16       0.04           26.80
## 546           3878        16       0.04           26.84
## 547           3899        16       0.04           26.88
## 548           3905        16       0.04           26.92
## 549           3909        16       0.04           26.96
## 550           3911        16       0.04           27.00
## 551           3938        16       0.04           27.04
## 552           3956        16       0.04           27.08
## 553           3967        16       0.04           27.12
## 554           3973        16       0.04           27.16
## 555           4042        16       0.04           27.20
## 556           4056        16       0.04           27.24
## 557           4078        16       0.04           27.28
## 558           4104        16       0.04           27.32
## 559           4110        16       0.04           27.36
## 560           4130        16       0.04           27.40
## 561           4152        16       0.04           27.44
## 562           4220        16       0.04           27.48
## 563           4243        16       0.04           27.52
## 564           4291        16       0.04           27.56
## 565           4372        16       0.04           27.60
## 566           4416        16       0.04           27.64
## 567           4441        16       0.04           27.68
## 568           4455        16       0.04           27.72
## 569           4550        16       0.04           27.76
## 570           4573        16       0.04           27.80
## 571           4579        16       0.04           27.84
## 572           4589        16       0.04           27.88
## 573           4592        16       0.04           27.92
## 574           4643        16       0.04           27.96
## 575           4662        16       0.04           28.00
## 576           4688        16       0.04           28.04
## 577           4700        16       0.04           28.08
## 578           4719        16       0.04           28.12
## 579           4747        16       0.04           28.16
## 580           4779        16       0.04           28.20
## 581           4915        16       0.04           28.24
## 582           4937        16       0.04           28.28
## 583           4938        16       0.04           28.32
## 584           4953        16       0.04           28.36
## 585           4999        16       0.04           28.40
## 586           1006        15       0.04           28.44
## 587           1160        15       0.04           28.48
## 588           1277        15       0.04           28.52
## 589           1278        15       0.04           28.56
## 590           1322        15       0.04           28.60
## 591           1332        15       0.04           28.64
## 592           1381        15       0.04           28.68
## 593           1384        15       0.04           28.72
## 594           1385        15       0.04           28.76
## 595           1419        15       0.04           28.80
## 596           1435        15       0.04           28.84
## 597           1452        15       0.04           28.88
## 598           1468        15       0.04           28.92
## 599           1493        15       0.04           28.96
## 600           1554        15       0.04           29.00
## 601           1603        15       0.04           29.04
## 602           1609        15       0.04           29.08
## 603           1613        15       0.04           29.12
## 604           1628        15       0.04           29.16
## 605           1659        15       0.04           29.20
## 606           1692        15       0.04           29.24
## 607           1697        15       0.04           29.28
## 608           1729        15       0.04           29.32
## 609           1757        15       0.04           29.36
## 610           1844        15       0.04           29.40
## 611           1862        15       0.04           29.44
## 612           1892        15       0.04           29.48
## 613           1949        15       0.04           29.52
## 614           1967        15       0.04           29.56
## 615           2040        15       0.04           29.60
## 616           2041        15       0.04           29.64
## 617           2045        15       0.04           29.68
## 618           2077        15       0.04           29.72
## 619           2100        15       0.04           29.76
## 620           2166        15       0.04           29.80
## 621           2194        15       0.04           29.84
## 622           2231        15       0.04           29.88
## 623           2244        15       0.04           29.92
## 624           2267        15       0.04           29.96
## 625           2325        15       0.04           30.00
## 626           2346        15       0.04           30.04
## 627           2364        15       0.04           30.08
## 628           2391        15       0.04           30.12
## 629           2437        15       0.04           30.16
## 630           2441        15       0.04           30.20
## 631           2453        15       0.04           30.24
## 632           2499        15       0.04           30.28
## 633           2523        15       0.04           30.32
## 634           2597        15       0.04           30.36
## 635           2599        15       0.04           30.40
## 636           2689        15       0.04           30.44
## 637           2715        15       0.04           30.48
## 638           2745        15       0.04           30.52
## 639           2746        15       0.04           30.56
## 640           2755        15       0.04           30.60
## 641           2761        15       0.04           30.64
## 642           2792        15       0.04           30.68
## 643           2840        15       0.04           30.72
## 644           2857        15       0.04           30.76
## 645           2867        15       0.04           30.80
## 646           2910        15       0.04           30.84
## 647           2916        15       0.04           30.88
## 648           2950        15       0.04           30.92
## 649           2952        15       0.04           30.96
## 650           2955        15       0.04           31.00
## 651           2993        15       0.04           31.04
## 652           3026        15       0.04           31.08
## 653           3028        15       0.04           31.12
## 654           3031        15       0.04           31.16
## 655           3051        15       0.04           31.20
## 656           3071        15       0.04           31.24
## 657           3081        15       0.04           31.28
## 658           3207        15       0.04           31.32
## 659           3214        15       0.04           31.36
## 660           3227        15       0.04           31.40
## 661           3276        15       0.04           31.44
## 662           3354        15       0.04           31.48
## 663           3365        15       0.04           31.52
## 664           3369        15       0.04           31.56
## 665           3399        15       0.04           31.60
## 666           3476        15       0.04           31.64
## 667           3483        15       0.04           31.68
## 668           3489        15       0.04           31.72
## 669           3505        15       0.04           31.76
## 670           3529        15       0.04           31.80
## 671           3535        15       0.04           31.84
## 672           3548        15       0.04           31.88
## 673           3583        15       0.04           31.92
## 674           3600        15       0.04           31.96
## 675           3604        15       0.04           32.00
## 676           3620        15       0.04           32.04
## 677           3643        15       0.04           32.08
## 678           3688        15       0.04           32.12
## 679           3760        15       0.04           32.16
## 680           3775        15       0.04           32.20
## 681           3779        15       0.04           32.24
## 682           3797        15       0.04           32.28
## 683           3818        15       0.04           32.32
## 684           3832        15       0.04           32.36
## 685           3864        15       0.04           32.40
## 686           3948        15       0.04           32.44
## 687           3950        15       0.04           32.48
## 688           3971        15       0.04           32.52
## 689           3982        15       0.04           32.56
## 690           3985        15       0.04           32.60
## 691           4117        15       0.04           32.64
## 692           4121        15       0.04           32.68
## 693           4146        15       0.04           32.72
## 694           4163        15       0.04           32.76
## 695           4169        15       0.04           32.80
## 696           4170        15       0.04           32.84
## 697           4192        15       0.04           32.88
## 698           4206        15       0.04           32.92
## 699           4207        15       0.04           32.96
## 700           4240        15       0.04           33.00
## 701           4275        15       0.04           33.04
## 702           4280        15       0.04           33.08
## 703           4299        15       0.04           33.12
## 704           4301        15       0.04           33.16
## 705           4305        15       0.04           33.20
## 706           4320        15       0.04           33.24
## 707           4334        15       0.04           33.28
## 708           4336        15       0.04           33.32
## 709           4362        15       0.04           33.36
## 710           4417        15       0.04           33.40
## 711           4426        15       0.04           33.44
## 712           4434        15       0.04           33.48
## 713           4444        15       0.04           33.52
## 714           4445        15       0.04           33.56
## 715           4499        15       0.04           33.60
## 716           4512        15       0.04           33.64
## 717           4525        15       0.04           33.68
## 718           4548        15       0.04           33.72
## 719           4601        15       0.04           33.76
## 720           4685        15       0.04           33.80
## 721           4692        15       0.04           33.84
## 722           4717        15       0.04           33.88
## 723           4742        15       0.04           33.92
## 724           4744        15       0.04           33.96
## 725           4778        15       0.04           34.00
## 726           4800        15       0.04           34.04
## 727           4812        15       0.04           34.08
## 728           4814        15       0.04           34.12
## 729           4952        15       0.04           34.16
## 730           1035        14       0.04           34.20
## 731           1050        14       0.04           34.24
## 732           1061        14       0.04           34.28
## 733           1065        14       0.04           34.32
## 734           1077        14       0.04           34.36
## 735           1086        14       0.04           34.40
## 736           1176        14       0.04           34.44
## 737           1206        14       0.04           34.48
## 738           1216        14       0.04           34.52
## 739           1230        14       0.04           34.56
## 740           1259        14       0.04           34.60
## 741           1269        14       0.04           34.64
## 742           1285        14       0.04           34.68
## 743           1303        14       0.04           34.72
## 744           1312        14       0.04           34.76
## 745           1324        14       0.04           34.80
## 746           1340        14       0.04           34.84
## 747           1347        14       0.04           34.88
## 748           1373        14       0.04           34.92
## 749           1416        14       0.04           34.96
## 750           1479        14       0.04           35.00
## 751           1527        14       0.04           35.04
## 752           1553        14       0.04           35.08
## 753           1599        14       0.04           35.12
## 754           1602        14       0.04           35.16
## 755           1621        14       0.04           35.20
## 756           1632        14       0.04           35.24
## 757           1703        14       0.04           35.28
## 758           1706        14       0.04           35.32
## 759           1722        14       0.04           35.36
## 760           1743        14       0.04           35.40
## 761           1754        14       0.04           35.44
## 762           1758        14       0.04           35.48
## 763           1776        14       0.04           35.52
## 764           1796        14       0.04           35.56
## 765           1863        14       0.04           35.60
## 766           1865        14       0.04           35.64
## 767           1888        14       0.04           35.68
## 768           1894        14       0.04           35.72
## 769           1921        14       0.04           35.76
## 770           1924        14       0.04           35.80
## 771           1939        14       0.04           35.84
## 772           1945        14       0.04           35.88
## 773           1969        14       0.04           35.92
## 774           1994        14       0.04           35.96
## 775           2031        14       0.04           36.00
## 776           2042        14       0.04           36.04
## 777           2065        14       0.04           36.08
## 778           2079        14       0.04           36.12
## 779           2120        14       0.04           36.16
## 780           2196        14       0.04           36.20
## 781           2201        14       0.04           36.24
## 782           2209        14       0.04           36.28
## 783           2215        14       0.04           36.32
## 784           2232        14       0.04           36.36
## 785           2236        14       0.04           36.40
## 786           2265        14       0.04           36.44
## 787           2273        14       0.04           36.48
## 788           2315        14       0.04           36.52
## 789           2356        14       0.04           36.56
## 790           2362        14       0.04           36.60
## 791           2374        14       0.04           36.64
## 792           2390        14       0.04           36.68
## 793           2393        14       0.04           36.72
## 794           2413        14       0.04           36.76
## 795           2415        14       0.04           36.80
## 796           2432        14       0.04           36.84
## 797           2475        14       0.04           36.88
## 798           2484        14       0.04           36.92
## 799           2502        14       0.04           36.96
## 800           2510        14       0.04           37.00
## 801           2519        14       0.04           37.04
## 802           2534        14       0.04           37.08
## 803           2553        14       0.04           37.12
## 804           2563        14       0.04           37.16
## 805           2604        14       0.04           37.20
## 806           2676        14       0.04           37.24
## 807           2711        14       0.04           37.28
## 808           2719        14       0.04           37.32
## 809           2860        14       0.04           37.36
## 810           2869        14       0.04           37.40
## 811           2885        14       0.04           37.44
## 812           2930        14       0.04           37.48
## 813           2944        14       0.04           37.52
## 814           2996        14       0.04           37.56
## 815           3009        14       0.04           37.60
## 816           3041        14       0.04           37.64
## 817           3084        14       0.04           37.68
## 818           3101        14       0.04           37.72
## 819           3107        14       0.04           37.76
## 820           3116        14       0.04           37.80
## 821           3166        14       0.04           37.84
## 822           3175        14       0.04           37.88
## 823           3181        14       0.04           37.92
## 824           3182        14       0.04           37.96
## 825           3184        14       0.04           38.00
## 826           3194        14       0.04           38.04
## 827           3208        14       0.04           38.08
## 828           3296        14       0.04           38.12
## 829           3321        14       0.04           38.16
## 830           3327        14       0.04           38.20
## 831           3347        14       0.04           38.24
## 832           3348        14       0.04           38.28
## 833           3410        14       0.04           38.32
## 834           3416        14       0.04           38.36
## 835           3437        14       0.04           38.40
## 836           3491        14       0.04           38.44
## 837           3509        14       0.04           38.48
## 838           3511        14       0.04           38.52
## 839           3539        14       0.04           38.56
## 840           3571        14       0.04           38.60
## 841           3574        14       0.04           38.64
## 842           3584        14       0.04           38.68
## 843           3590        14       0.04           38.72
## 844           3592        14       0.04           38.76
## 845           3608        14       0.04           38.80
## 846           3612        14       0.04           38.84
## 847           3683        14       0.04           38.88
## 848           3758        14       0.04           38.92
## 849           3817        14       0.04           38.96
## 850           3848        14       0.04           39.00
## 851           3857        14       0.04           39.04
## 852           3863        14       0.04           39.08
## 853           3881        14       0.04           39.12
## 854           3900        14       0.04           39.16
## 855           3910        14       0.04           39.20
## 856           3924        14       0.04           39.24
## 857           3959        14       0.04           39.28
## 858           3962        14       0.04           39.32
## 859           3963        14       0.04           39.36
## 860           3972        14       0.04           39.40
## 861           4002        14       0.04           39.44
## 862           4012        14       0.04           39.48
## 863           4024        14       0.04           39.52
## 864           4038        14       0.04           39.56
## 865           4073        14       0.04           39.60
## 866           4077        14       0.04           39.64
## 867           4091        14       0.04           39.68
## 868           4097        14       0.04           39.72
## 869           4108        14       0.04           39.76
## 870           4134        14       0.04           39.80
## 871           4162        14       0.04           39.84
## 872           4166        14       0.04           39.88
## 873           4182        14       0.04           39.92
## 874           4194        14       0.04           39.96
## 875           4236        14       0.04           40.00
## 876           4267        14       0.04           40.04
## 877           4294        14       0.04           40.08
## 878           4319        14       0.04           40.12
## 879           4324        14       0.04           40.16
## 880           4384        14       0.04           40.20
## 881           4388        14       0.04           40.24
## 882           4391        14       0.04           40.28
## 883           4430        14       0.04           40.32
## 884           4431        14       0.04           40.36
## 885           4442        14       0.04           40.40
## 886           4470        14       0.04           40.44
## 887           4473        14       0.04           40.48
## 888           4504        14       0.04           40.52
## 889           4555        14       0.04           40.56
## 890           4576        14       0.04           40.60
## 891           4623        14       0.04           40.64
## 892           4633        14       0.04           40.68
## 893           4681        14       0.04           40.72
## 894           4708        14       0.04           40.76
## 895           4746        14       0.04           40.80
## 896           4756        14       0.04           40.84
## 897           4796        14       0.04           40.88
## 898           4821        14       0.04           40.92
## 899           4825        14       0.04           40.96
## 900           4827        14       0.04           41.00
## 901           4835        14       0.04           41.04
## 902           4851        14       0.04           41.08
## 903           4860        14       0.04           41.12
## 904           4924        14       0.04           41.16
## 905           4929        14       0.04           41.20
## 906           4931        14       0.04           41.24
## 907           4932        14       0.04           41.28
## 908           4947        14       0.04           41.32
## 909           1000        13       0.03           41.35
## 910           1011        13       0.03           41.38
## 911           1028        13       0.03           41.41
## 912           1076        13       0.03           41.44
## 913           1129        13       0.03           41.47
## 914           1133        13       0.03           41.50
## 915           1199        13       0.03           41.53
## 916           1213        13       0.03           41.56
## 917           1240        13       0.03           41.59
## 918           1276        13       0.03           41.62
## 919           1290        13       0.03           41.65
## 920           1339        13       0.03           41.68
## 921           1342        13       0.03           41.71
## 922           1354        13       0.03           41.74
## 923           1355        13       0.03           41.77
## 924           1363        13       0.03           41.80
## 925           1370        13       0.03           41.83
## 926           1391        13       0.03           41.86
## 927           1428        13       0.03           41.89
## 928           1442        13       0.03           41.92
## 929           1476        13       0.03           41.95
## 930           1480        13       0.03           41.98
## 931           1489        13       0.03           42.01
## 932           1515        13       0.03           42.04
## 933           1542        13       0.03           42.07
## 934           1551        13       0.03           42.10
## 935           1587        13       0.03           42.13
## 936           1616        13       0.03           42.16
## 937           1663        13       0.03           42.19
## 938           1696        13       0.03           42.22
## 939           1702        13       0.03           42.25
## 940           1719        13       0.03           42.28
## 941           1726        13       0.03           42.31
## 942           1741        13       0.03           42.34
## 943           1782        13       0.03           42.37
## 944           1787        13       0.03           42.40
## 945           1792        13       0.03           42.43
## 946           1822        13       0.03           42.46
## 947           1825        13       0.03           42.49
## 948           1855        13       0.03           42.52
## 949           1895        13       0.03           42.55
## 950           1930        13       0.03           42.58
## 951           1937        13       0.03           42.61
## 952           2004        13       0.03           42.64
## 953           2005        13       0.03           42.67
## 954           2018        13       0.03           42.70
## 955           2028        13       0.03           42.73
## 956           2063        13       0.03           42.76
## 957           2072        13       0.03           42.79
## 958           2117        13       0.03           42.82
## 959           2175        13       0.03           42.85
## 960           2176        13       0.03           42.88
## 961           2202        13       0.03           42.91
## 962           2211        13       0.03           42.94
## 963           2218        13       0.03           42.97
## 964           2226        13       0.03           43.00
## 965           2235        13       0.03           43.03
## 966           2238        13       0.03           43.06
## 967           2261        13       0.03           43.09
## 968           2272        13       0.03           43.12
## 969           2284        13       0.03           43.15
## 970           2306        13       0.03           43.18
## 971           2321        13       0.03           43.21
## 972           2331        13       0.03           43.24
## 973           2332        13       0.03           43.27
## 974           2337        13       0.03           43.30
## 975           2359        13       0.03           43.33
## 976           2366        13       0.03           43.36
## 977           2403        13       0.03           43.39
## 978           2431        13       0.03           43.42
## 979           2459        13       0.03           43.45
## 980           2469        13       0.03           43.48
## 981           2480        13       0.03           43.51
## 982           2507        13       0.03           43.54
## 983           2535        13       0.03           43.57
## 984           2552        13       0.03           43.60
## 985           2587        13       0.03           43.63
## 986           2648        13       0.03           43.66
## 987           2652        13       0.03           43.69
## 988           2688        13       0.03           43.72
## 989           2712        13       0.03           43.75
## 990           2764        13       0.03           43.78
## 991           2781        13       0.03           43.81
## 992           2784        13       0.03           43.84
## 993           2800        13       0.03           43.87
## 994           2847        13       0.03           43.90
## 995           2870        13       0.03           43.93
## 996           2879        13       0.03           43.96
## 997           2975        13       0.03           43.99
## 998           3013        13       0.03           44.02
## 999           3035        13       0.03           44.05
## 1000          3138        13       0.03           44.08
## 1001          3144        13       0.03           44.11
## 1002          3176        13       0.03           44.14
## 1003          3193        13       0.03           44.17
## 1004          3205        13       0.03           44.20
## 1005          3237        13       0.03           44.23
## 1006          3258        13       0.03           44.26
## 1007          3287        13       0.03           44.29
## 1008          3294        13       0.03           44.32
## 1009          3315        13       0.03           44.35
## 1010          3325        13       0.03           44.38
## 1011          3329        13       0.03           44.41
## 1012          3363        13       0.03           44.44
## 1013          3389        13       0.03           44.47
## 1014          3396        13       0.03           44.50
## 1015          3409        13       0.03           44.53
## 1016          3414        13       0.03           44.56
## 1017          3442        13       0.03           44.59
## 1018          3447        13       0.03           44.62
## 1019          3456        13       0.03           44.65
## 1020          3467        13       0.03           44.68
## 1021          3519        13       0.03           44.71
## 1022          3537        13       0.03           44.74
## 1023          3552        13       0.03           44.77
## 1024          3579        13       0.03           44.80
## 1025          3588        13       0.03           44.83
## 1026          3589        13       0.03           44.86
## 1027          3629        13       0.03           44.89
## 1028          3637        13       0.03           44.92
## 1029          3668        13       0.03           44.95
## 1030          3672        13       0.03           44.98
## 1031          3677        13       0.03           45.01
## 1032          3684        13       0.03           45.04
## 1033          3727        13       0.03           45.07
## 1034          3728        13       0.03           45.10
## 1035          3745        13       0.03           45.13
## 1036          3746        13       0.03           45.16
## 1037          3763        13       0.03           45.19
## 1038          3786        13       0.03           45.22
## 1039          3790        13       0.03           45.25
## 1040          3814        13       0.03           45.28
## 1041          3856        13       0.03           45.31
## 1042          3891        13       0.03           45.34
## 1043          3897        13       0.03           45.37
## 1044          3917        13       0.03           45.40
## 1045          3918        13       0.03           45.43
## 1046          3931        13       0.03           45.46
## 1047          3946        13       0.03           45.49
## 1048          3976        13       0.03           45.52
## 1049          3999        13       0.03           45.55
## 1050          4035        13       0.03           45.58
## 1051          4065        13       0.03           45.61
## 1052          4086        13       0.03           45.64
## 1053          4106        13       0.03           45.67
## 1054          4109        13       0.03           45.70
## 1055          4133        13       0.03           45.73
## 1056          4156        13       0.03           45.76
## 1057          4160        13       0.03           45.79
## 1058          4180        13       0.03           45.82
## 1059          4191        13       0.03           45.85
## 1060          4202        13       0.03           45.88
## 1061          4214        13       0.03           45.91
## 1062          4222        13       0.03           45.94
## 1063          4228        13       0.03           45.97
## 1064          4257        13       0.03           46.00
## 1065          4258        13       0.03           46.03
## 1066          4281        13       0.03           46.06
## 1067          4286        13       0.03           46.09
## 1068          4340        13       0.03           46.12
## 1069          4351        13       0.03           46.15
## 1070          4352        13       0.03           46.18
## 1071          4392        13       0.03           46.21
## 1072          4412        13       0.03           46.24
## 1073          4501        13       0.03           46.27
## 1074          4505        13       0.03           46.30
## 1075          4508        13       0.03           46.33
## 1076          4537        13       0.03           46.36
## 1077          4566        13       0.03           46.39
## 1078          4606        13       0.03           46.42
## 1079          4616        13       0.03           46.45
## 1080          4652        13       0.03           46.48
## 1081          4676        13       0.03           46.51
## 1082          4686        13       0.03           46.54
## 1083          4718        13       0.03           46.57
## 1084          4720        13       0.03           46.60
## 1085          4743        13       0.03           46.63
## 1086          4757        13       0.03           46.66
## 1087          4762        13       0.03           46.69
## 1088          4788        13       0.03           46.72
## 1089          4807        13       0.03           46.75
## 1090          4826        13       0.03           46.78
## 1091          4832        13       0.03           46.81
## 1092          4868        13       0.03           46.84
## 1093          4891        13       0.03           46.87
## 1094          4916        13       0.03           46.90
## 1095          4923        13       0.03           46.93
## 1096          4951        13       0.03           46.96
## 1097          4958        13       0.03           46.99
## 1098          4969        13       0.03           47.02
## 1099          4972        13       0.03           47.05
## 1100          4975        13       0.03           47.08
## 1101          1001        12       0.03           47.11
## 1102          1008        12       0.03           47.14
## 1103          1010        12       0.03           47.17
## 1104          1033        12       0.03           47.20
## 1105          1053        12       0.03           47.23
## 1106          1073        12       0.03           47.26
## 1107          1090        12       0.03           47.29
## 1108          1108        12       0.03           47.32
## 1109          1109        12       0.03           47.35
## 1110          1127        12       0.03           47.38
## 1111          1143        12       0.03           47.41
## 1112          1162        12       0.03           47.44
## 1113          1256        12       0.03           47.47
## 1114          1291        12       0.03           47.50
## 1115          1294        12       0.03           47.53
## 1116          1305        12       0.03           47.56
## 1117          1307        12       0.03           47.59
## 1118          1335        12       0.03           47.62
## 1119          1341        12       0.03           47.65
## 1120          1358        12       0.03           47.68
## 1121          1365        12       0.03           47.71
## 1122          1390        12       0.03           47.74
## 1123          1406        12       0.03           47.77
## 1124          1412        12       0.03           47.80
## 1125          1440        12       0.03           47.83
## 1126          1457        12       0.03           47.86
## 1127          1474        12       0.03           47.89
## 1128          1540        12       0.03           47.92
## 1129          1615        12       0.03           47.95
## 1130          1623        12       0.03           47.98
## 1131          1636        12       0.03           48.01
## 1132          1641        12       0.03           48.04
## 1133          1652        12       0.03           48.07
## 1134          1656        12       0.03           48.10
## 1135          1658        12       0.03           48.13
## 1136          1674        12       0.03           48.16
## 1137          1693        12       0.03           48.19
## 1138          1731        12       0.03           48.22
## 1139          1736        12       0.03           48.25
## 1140          1750        12       0.03           48.28
## 1141          1759        12       0.03           48.31
## 1142          1767        12       0.03           48.34
## 1143          1774        12       0.03           48.37
## 1144          1800        12       0.03           48.40
## 1145          1810        12       0.03           48.43
## 1146          1814        12       0.03           48.46
## 1147          1817        12       0.03           48.49
## 1148          1837        12       0.03           48.52
## 1149          1846        12       0.03           48.55
## 1150          1884        12       0.03           48.58
## 1151          1896        12       0.03           48.61
## 1152          1899        12       0.03           48.64
## 1153          1901        12       0.03           48.67
## 1154          1923        12       0.03           48.70
## 1155          1946        12       0.03           48.73
## 1156          1961        12       0.03           48.76
## 1157          2010        12       0.03           48.79
## 1158          2047        12       0.03           48.82
## 1159          2048        12       0.03           48.85
## 1160          2054        12       0.03           48.88
## 1161          2058        12       0.03           48.91
## 1162          2066        12       0.03           48.94
## 1163          2068        12       0.03           48.97
## 1164          2083        12       0.03           49.00
## 1165          2102        12       0.03           49.03
## 1166          2106        12       0.03           49.06
## 1167          2127        12       0.03           49.09
## 1168          2131        12       0.03           49.12
## 1169          2139        12       0.03           49.15
## 1170          2152        12       0.03           49.18
## 1171          2160        12       0.03           49.21
## 1172          2165        12       0.03           49.24
## 1173          2204        12       0.03           49.27
## 1174          2212        12       0.03           49.30
## 1175          2239        12       0.03           49.33
## 1176          2240        12       0.03           49.36
## 1177          2242        12       0.03           49.39
## 1178          2254        12       0.03           49.42
## 1179          2255        12       0.03           49.45
## 1180          2288        12       0.03           49.48
## 1181          2291        12       0.03           49.51
## 1182          2309        12       0.03           49.54
## 1183          2355        12       0.03           49.57
## 1184          2383        12       0.03           49.60
## 1185          2386        12       0.03           49.63
## 1186          2400        12       0.03           49.66
## 1187          2430        12       0.03           49.69
## 1188          2435        12       0.03           49.72
## 1189          2467        12       0.03           49.75
## 1190          2513        12       0.03           49.78
## 1191          2515        12       0.03           49.81
## 1192          2518        12       0.03           49.84
## 1193          2532        12       0.03           49.87
## 1194          2545        12       0.03           49.90
## 1195          2547        12       0.03           49.93
## 1196          2565        12       0.03           49.96
## 1197          2580        12       0.03           49.99
## 1198          2581        12       0.03           50.02
## 1199          2582        12       0.03           50.05
## 1200          2622        12       0.03           50.08
## 1201          2641        12       0.03           50.11
## 1202          2643        12       0.03           50.14
## 1203          2653        12       0.03           50.17
## 1204          2672        12       0.03           50.20
## 1205          2685        12       0.03           50.23
## 1206          2741        12       0.03           50.26
## 1207          2747        12       0.03           50.29
## 1208          2751        12       0.03           50.32
## 1209          2765        12       0.03           50.35
## 1210          2769        12       0.03           50.38
## 1211          2795        12       0.03           50.41
## 1212          2796        12       0.03           50.44
## 1213          2836        12       0.03           50.47
## 1214          2861        12       0.03           50.50
## 1215          2876        12       0.03           50.53
## 1216          2900        12       0.03           50.56
## 1217          2903        12       0.03           50.59
## 1218          2941        12       0.03           50.62
## 1219          2942        12       0.03           50.65
## 1220          2964        12       0.03           50.68
## 1221          2973        12       0.03           50.71
## 1222          2977        12       0.03           50.74
## 1223          2982        12       0.03           50.77
## 1224          2989        12       0.03           50.80
## 1225          2991        12       0.03           50.83
## 1226          3038        12       0.03           50.86
## 1227          3066        12       0.03           50.89
## 1228          3086        12       0.03           50.92
## 1229          3099        12       0.03           50.95
## 1230          3100        12       0.03           50.98
## 1231          3113        12       0.03           51.01
## 1232          3117        12       0.03           51.04
## 1233          3140        12       0.03           51.07
## 1234          3168        12       0.03           51.10
## 1235          3170        12       0.03           51.13
## 1236          3178        12       0.03           51.16
## 1237          3190        12       0.03           51.19
## 1238          3203        12       0.03           51.22
## 1239          3206        12       0.03           51.25
## 1240          3220        12       0.03           51.28
## 1241          3229        12       0.03           51.31
## 1242          3252        12       0.03           51.34
## 1243          3297        12       0.03           51.37
## 1244          3344        12       0.03           51.40
## 1245          3364        12       0.03           51.43
## 1246          3400        12       0.03           51.46
## 1247          3472        12       0.03           51.49
## 1248          3480        12       0.03           51.52
## 1249          3486        12       0.03           51.55
## 1250          3487        12       0.03           51.58
## 1251          3515        12       0.03           51.61
## 1252          3524        12       0.03           51.64
## 1253          3527        12       0.03           51.67
## 1254          3528        12       0.03           51.70
## 1255          3559        12       0.03           51.73
## 1256          3596        12       0.03           51.76
## 1257          3603        12       0.03           51.79
## 1258          3613        12       0.03           51.82
## 1259          3642        12       0.03           51.85
## 1260          3661        12       0.03           51.88
## 1261          3666        12       0.03           51.91
## 1262          3669        12       0.03           51.94
## 1263          3690        12       0.03           51.97
## 1264          3692        12       0.03           52.00
## 1265          3701        12       0.03           52.03
## 1266          3703        12       0.03           52.06
## 1267          3704        12       0.03           52.09
## 1268          3736        12       0.03           52.12
## 1269          3744        12       0.03           52.15
## 1270          3764        12       0.03           52.18
## 1271          3774        12       0.03           52.21
## 1272          3778        12       0.03           52.24
## 1273          3831        12       0.03           52.27
## 1274          3846        12       0.03           52.30
## 1275          3849        12       0.03           52.33
## 1276          3882        12       0.03           52.36
## 1277          3894        12       0.03           52.39
## 1278          3913        12       0.03           52.42
## 1279          3986        12       0.03           52.45
## 1280          4006        12       0.03           52.48
## 1281          4007        12       0.03           52.51
## 1282          4025        12       0.03           52.54
## 1283          4036        12       0.03           52.57
## 1284          4039        12       0.03           52.60
## 1285          4049        12       0.03           52.63
## 1286          4068        12       0.03           52.66
## 1287          4076        12       0.03           52.69
## 1288          4107        12       0.03           52.72
## 1289          4113        12       0.03           52.75
## 1290          4138        12       0.03           52.78
## 1291          4147        12       0.03           52.81
## 1292          4148        12       0.03           52.84
## 1293          4150        12       0.03           52.87
## 1294          4201        12       0.03           52.90
## 1295          4211        12       0.03           52.93
## 1296          4218        12       0.03           52.96
## 1297          4224        12       0.03           52.99
## 1298          4232        12       0.03           53.02
## 1299          4259        12       0.03           53.05
## 1300          4260        12       0.03           53.08
## 1301          4261        12       0.03           53.11
## 1302          4268        12       0.03           53.14
## 1303          4274        12       0.03           53.17
## 1304          4288        12       0.03           53.20
## 1305          4306        12       0.03           53.23
## 1306          4323        12       0.03           53.26
## 1307          4326        12       0.03           53.29
## 1308          4328        12       0.03           53.32
## 1309          4348        12       0.03           53.35
## 1310          4367        12       0.03           53.38
## 1311          4375        12       0.03           53.41
## 1312          4403        12       0.03           53.44
## 1313          4427        12       0.03           53.47
## 1314          4440        12       0.03           53.50
## 1315          4448        12       0.03           53.53
## 1316          4459        12       0.03           53.56
## 1317          4462        12       0.03           53.59
## 1318          4485        12       0.03           53.62
## 1319          4523        12       0.03           53.65
## 1320          4540        12       0.03           53.68
## 1321          4544        12       0.03           53.71
## 1322          4563        12       0.03           53.74
## 1323          4567        12       0.03           53.77
## 1324          4569        12       0.03           53.80
## 1325          4608        12       0.03           53.83
## 1326          4610        12       0.03           53.86
## 1327          4613        12       0.03           53.89
## 1328          4618        12       0.03           53.92
## 1329          4646        12       0.03           53.95
## 1330          4678        12       0.03           53.98
## 1331          4697        12       0.03           54.01
## 1332          4715        12       0.03           54.04
## 1333          4735        12       0.03           54.07
## 1334          4748        12       0.03           54.10
## 1335          4759        12       0.03           54.13
## 1336          4761        12       0.03           54.16
## 1337          4769        12       0.03           54.19
## 1338          4785        12       0.03           54.22
## 1339          4787        12       0.03           54.25
## 1340          4809        12       0.03           54.28
## 1341          4817        12       0.03           54.31
## 1342          4819        12       0.03           54.34
## 1343          4822        12       0.03           54.37
## 1344          4842        12       0.03           54.40
## 1345          4853        12       0.03           54.43
## 1346          4862        12       0.03           54.46
## 1347          4872        12       0.03           54.49
## 1348          4890        12       0.03           54.52
## 1349          4892        12       0.03           54.55
## 1350          4959        12       0.03           54.58
## 1351          4967        12       0.03           54.61
## 1352          4986        12       0.03           54.64
## 1353          1012        11       0.03           54.67
## 1354          1016        11       0.03           54.70
## 1355          1017        11       0.03           54.73
## 1356          1040        11       0.03           54.76
## 1357          1075        11       0.03           54.79
## 1358          1111        11       0.03           54.82
## 1359          1113        11       0.03           54.85
## 1360          1123        11       0.03           54.88
## 1361          1125        11       0.03           54.91
## 1362          1130        11       0.03           54.94
## 1363          1158        11       0.03           54.97
## 1364          1174        11       0.03           55.00
## 1365          1178        11       0.03           55.03
## 1366          1208        11       0.03           55.06
## 1367          1241        11       0.03           55.09
## 1368          1289        11       0.03           55.12
## 1369          1293        11       0.03           55.15
## 1370          1309        11       0.03           55.18
## 1371          1326        11       0.03           55.21
## 1372          1330        11       0.03           55.24
## 1373          1349        11       0.03           55.27
## 1374          1374        11       0.03           55.30
## 1375          1377        11       0.03           55.33
## 1376          1380        11       0.03           55.36
## 1377          1420        11       0.03           55.39
## 1378          1421        11       0.03           55.42
## 1379          1432        11       0.03           55.45
## 1380          1443        11       0.03           55.48
## 1381          1454        11       0.03           55.51
## 1382          1491        11       0.03           55.54
## 1383          1492        11       0.03           55.57
## 1384          1504        11       0.03           55.60
## 1385          1526        11       0.03           55.63
## 1386          1605        11       0.03           55.66
## 1387          1619        11       0.03           55.69
## 1388          1620        11       0.03           55.72
## 1389          1668        11       0.03           55.75
## 1390          1677        11       0.03           55.78
## 1391          1679        11       0.03           55.81
## 1392          1687        11       0.03           55.84
## 1393          1724        11       0.03           55.87
## 1394          1747        11       0.03           55.90
## 1395          1764        11       0.03           55.93
## 1396          1797        11       0.03           55.96
## 1397          1801        11       0.03           55.99
## 1398          1806        11       0.03           56.02
## 1399          1815        11       0.03           56.05
## 1400          1823        11       0.03           56.08
## 1401          1839        11       0.03           56.11
## 1402          1859        11       0.03           56.14
## 1403          1867        11       0.03           56.17
## 1404          1869        11       0.03           56.20
## 1405          1877        11       0.03           56.23
## 1406          1881        11       0.03           56.26
## 1407          1885        11       0.03           56.29
## 1408          1917        11       0.03           56.32
## 1409          1935        11       0.03           56.35
## 1410          1940        11       0.03           56.38
## 1411          1954        11       0.03           56.41
## 1412          1968        11       0.03           56.44
## 1413          2029        11       0.03           56.47
## 1414          2033        11       0.03           56.50
## 1415          2035        11       0.03           56.53
## 1416          2061        11       0.03           56.56
## 1417          2074        11       0.03           56.59
## 1418          2091        11       0.03           56.62
## 1419          2097        11       0.03           56.65
## 1420          2101        11       0.03           56.68
## 1421          2128        11       0.03           56.71
## 1422          2132        11       0.03           56.74
## 1423          2151        11       0.03           56.77
## 1424          2154        11       0.03           56.80
## 1425          2157        11       0.03           56.83
## 1426          2158        11       0.03           56.86
## 1427          2169        11       0.03           56.89
## 1428          2178        11       0.03           56.92
## 1429          2185        11       0.03           56.95
## 1430          2247        11       0.03           56.98
## 1431          2274        11       0.03           57.01
## 1432          2290        11       0.03           57.04
## 1433          2307        11       0.03           57.07
## 1434          2336        11       0.03           57.10
## 1435          2338        11       0.03           57.13
## 1436          2363        11       0.03           57.16
## 1437          2375        11       0.03           57.19
## 1438          2396        11       0.03           57.22
## 1439          2399        11       0.03           57.25
## 1440          2404        11       0.03           57.28
## 1441          2410        11       0.03           57.31
## 1442          2422        11       0.03           57.34
## 1443          2436        11       0.03           57.37
## 1444          2452        11       0.03           57.40
## 1445          2465        11       0.03           57.43
## 1446          2470        11       0.03           57.46
## 1447          2495        11       0.03           57.49
## 1448          2504        11       0.03           57.52
## 1449          2505        11       0.03           57.55
## 1450          2514        11       0.03           57.58
## 1451          2525        11       0.03           57.61
## 1452          2530        11       0.03           57.64
## 1453          2570        11       0.03           57.67
## 1454          2574        11       0.03           57.70
## 1455          2669        11       0.03           57.73
## 1456          2678        11       0.03           57.76
## 1457          2682        11       0.03           57.79
## 1458          2693        11       0.03           57.82
## 1459          2696        11       0.03           57.85
## 1460          2701        11       0.03           57.88
## 1461          2709        11       0.03           57.91
## 1462          2730        11       0.03           57.94
## 1463          2803        11       0.03           57.97
## 1464          2805        11       0.03           58.00
## 1465          2807        11       0.03           58.03
## 1466          2830        11       0.03           58.06
## 1467          2832        11       0.03           58.09
## 1468          2837        11       0.03           58.12
## 1469          2849        11       0.03           58.15
## 1470          2854        11       0.03           58.18
## 1471          2882        11       0.03           58.21
## 1472          2893        11       0.03           58.24
## 1473          2899        11       0.03           58.27
## 1474          2906        11       0.03           58.30
## 1475          2909        11       0.03           58.33
## 1476          2912        11       0.03           58.36
## 1477          2920        11       0.03           58.39
## 1478          2924        11       0.03           58.42
## 1479          2940        11       0.03           58.45
## 1480          2956        11       0.03           58.48
## 1481          2984        11       0.03           58.51
## 1482          3005        11       0.03           58.54
## 1483          3010        11       0.03           58.57
## 1484          3011        11       0.03           58.60
## 1485          3025        11       0.03           58.63
## 1486          3045        11       0.03           58.66
## 1487          3062        11       0.03           58.69
## 1488          3089        11       0.03           58.72
## 1489          3142        11       0.03           58.75
## 1490          3148        11       0.03           58.78
## 1491          3154        11       0.03           58.81
## 1492          3185        11       0.03           58.84
## 1493          3204        11       0.03           58.87
## 1494          3209        11       0.03           58.90
## 1495          3257        11       0.03           58.93
## 1496          3282        11       0.03           58.96
## 1497          3299        11       0.03           58.99
## 1498          3300        11       0.03           59.02
## 1499          3307        11       0.03           59.05
## 1500          3310        11       0.03           59.08
## 1501          3323        11       0.03           59.11
## 1502          3324        11       0.03           59.14
## 1503          3328        11       0.03           59.17
## 1504          3360        11       0.03           59.20
## 1505          3370        11       0.03           59.23
## 1506          3385        11       0.03           59.26
## 1507          3390        11       0.03           59.29
## 1508          3398        11       0.03           59.32
## 1509          3421        11       0.03           59.35
## 1510          3424        11       0.03           59.38
## 1511          3439        11       0.03           59.41
## 1512          3468        11       0.03           59.44
## 1513          3502        11       0.03           59.47
## 1514          3520        11       0.03           59.50
## 1515          3545        11       0.03           59.53
## 1516          3557        11       0.03           59.56
## 1517          3570        11       0.03           59.59
## 1518          3575        11       0.03           59.62
## 1519          3587        11       0.03           59.65
## 1520          3599        11       0.03           59.68
## 1521          3617        11       0.03           59.71
## 1522          3645        11       0.03           59.74
## 1523          3653        11       0.03           59.77
## 1524          3674        11       0.03           59.80
## 1525          3675        11       0.03           59.83
## 1526          3694        11       0.03           59.86
## 1527          3697        11       0.03           59.89
## 1528          3698        11       0.03           59.92
## 1529          3705        11       0.03           59.95
## 1530          3748        11       0.03           59.98
## 1531          3762        11       0.03           60.01
## 1532          3769        11       0.03           60.04
## 1533          3789        11       0.03           60.07
## 1534          3794        11       0.03           60.10
## 1535          3847        11       0.03           60.13
## 1536          3893        11       0.03           60.16
## 1537          3896        11       0.03           60.19
## 1538          3920        11       0.03           60.22
## 1539          3934        11       0.03           60.25
## 1540          3966        11       0.03           60.28
## 1541          3980        11       0.03           60.31
## 1542          3983        11       0.03           60.34
## 1543          3987        11       0.03           60.37
## 1544          4009        11       0.03           60.40
## 1545          4040        11       0.03           60.43
## 1546          4041        11       0.03           60.46
## 1547          4045        11       0.03           60.49
## 1548          4069        11       0.03           60.52
## 1549          4082        11       0.03           60.55
## 1550          4084        11       0.03           60.58
## 1551          4098        11       0.03           60.61
## 1552          4115        11       0.03           60.64
## 1553          4120        11       0.03           60.67
## 1554          4125        11       0.03           60.70
## 1555          4127        11       0.03           60.73
## 1556          4131        11       0.03           60.76
## 1557          4199        11       0.03           60.79
## 1558          4212        11       0.03           60.82
## 1559          4216        11       0.03           60.85
## 1560          4233        11       0.03           60.88
## 1561          4249        11       0.03           60.91
## 1562          4255        11       0.03           60.94
## 1563          4295        11       0.03           60.97
## 1564          4322        11       0.03           61.00
## 1565          4377        11       0.03           61.03
## 1566          4380        11       0.03           61.06
## 1567          4397        11       0.03           61.09
## 1568          4410        11       0.03           61.12
## 1569          4467        11       0.03           61.15
## 1570          4474        11       0.03           61.18
## 1571          4482        11       0.03           61.21
## 1572          4498        11       0.03           61.24
## 1573          4503        11       0.03           61.27
## 1574          4527        11       0.03           61.30
## 1575          4536        11       0.03           61.33
## 1576          4546        11       0.03           61.36
## 1577          4600        11       0.03           61.39
## 1578          4637        11       0.03           61.42
## 1579          4649        11       0.03           61.45
## 1580          4650        11       0.03           61.48
## 1581          4704        11       0.03           61.51
## 1582          4734        11       0.03           61.54
## 1583          4736        11       0.03           61.57
## 1584          4750        11       0.03           61.60
## 1585          4789        11       0.03           61.63
## 1586          4790        11       0.03           61.66
## 1587          4794        11       0.03           61.69
## 1588          4797        11       0.03           61.72
## 1589          4806        11       0.03           61.75
## 1590          4808        11       0.03           61.78
## 1591          4841        11       0.03           61.81
## 1592          4843        11       0.03           61.84
## 1593          4867        11       0.03           61.87
## 1594          4895        11       0.03           61.90
## 1595          4906        11       0.03           61.93
## 1596          4925        11       0.03           61.96
## 1597          4962        11       0.03           61.99
## 1598          4992        11       0.03           62.02
## 1599          1014        10       0.03           62.05
## 1600          1020        10       0.03           62.08
## 1601          1037        10       0.03           62.11
## 1602          1041        10       0.03           62.14
## 1603          1069        10       0.03           62.17
## 1604          1074        10       0.03           62.20
## 1605          1100        10       0.03           62.23
## 1606          1102        10       0.03           62.26
## 1607          1103        10       0.03           62.29
## 1608          1104        10       0.03           62.32
## 1609          1128        10       0.03           62.35
## 1610          1132        10       0.03           62.38
## 1611          1135        10       0.03           62.41
## 1612          1150        10       0.03           62.44
## 1613          1171        10       0.03           62.47
## 1614          1185        10       0.03           62.50
## 1615          1202        10       0.03           62.53
## 1616          1205        10       0.03           62.56
## 1617          1223        10       0.03           62.59
## 1618          1226        10       0.03           62.62
## 1619          1234        10       0.03           62.65
## 1620          1252        10       0.03           62.68
## 1621          1282        10       0.03           62.71
## 1622          1302        10       0.03           62.74
## 1623          1320        10       0.03           62.77
## 1624          1328        10       0.03           62.80
## 1625          1343        10       0.03           62.83
## 1626          1345        10       0.03           62.86
## 1627          1356        10       0.03           62.89
## 1628          1372        10       0.03           62.92
## 1629          1403        10       0.03           62.95
## 1630          1417        10       0.03           62.98
## 1631          1425        10       0.03           63.01
## 1632          1426        10       0.03           63.04
## 1633          1460        10       0.03           63.07
## 1634          1473        10       0.03           63.10
## 1635          1475        10       0.03           63.13
## 1636          1499        10       0.03           63.16
## 1637          1501        10       0.03           63.19
## 1638          1512        10       0.03           63.22
## 1639          1513        10       0.03           63.25
## 1640          1514        10       0.03           63.28
## 1641          1517        10       0.03           63.31
## 1642          1523        10       0.03           63.34
## 1643          1524        10       0.03           63.37
## 1644          1575        10       0.03           63.40
## 1645          1591        10       0.03           63.43
## 1646          1596        10       0.03           63.46
## 1647          1611        10       0.03           63.49
## 1648          1622        10       0.03           63.52
## 1649          1648        10       0.03           63.55
## 1650          1664        10       0.03           63.58
## 1651          1676        10       0.03           63.61
## 1652          1699        10       0.03           63.64
## 1653          1723        10       0.03           63.67
## 1654          1746        10       0.03           63.70
## 1655          1751        10       0.03           63.73
## 1656          1752        10       0.03           63.76
## 1657          1770        10       0.03           63.79
## 1658          1789        10       0.03           63.82
## 1659          1808        10       0.03           63.85
## 1660          1816        10       0.03           63.88
## 1661          1818        10       0.03           63.91
## 1662          1820        10       0.03           63.94
## 1663          1833        10       0.03           63.97
## 1664          1835        10       0.03           64.00
## 1665          1838        10       0.03           64.03
## 1666          1851        10       0.03           64.06
## 1667          1852        10       0.03           64.09
## 1668          1872        10       0.03           64.12
## 1669          1883        10       0.03           64.15
## 1670          1900        10       0.03           64.18
## 1671          1903        10       0.03           64.21
## 1672          1910        10       0.03           64.24
## 1673          1938        10       0.03           64.27
## 1674          1950        10       0.03           64.30
## 1675          1952        10       0.03           64.33
## 1676          1962        10       0.03           64.36
## 1677          1964        10       0.03           64.39
## 1678          1980        10       0.03           64.42
## 1679          1996        10       0.03           64.45
## 1680          2038        10       0.03           64.48
## 1681          2069        10       0.03           64.51
## 1682          2071        10       0.03           64.54
## 1683          2081        10       0.03           64.57
## 1684          2082        10       0.03           64.60
## 1685          2087        10       0.03           64.63
## 1686          2109        10       0.03           64.66
## 1687          2122        10       0.03           64.69
## 1688          2144        10       0.03           64.72
## 1689          2148        10       0.03           64.75
## 1690          2162        10       0.03           64.78
## 1691          2170        10       0.03           64.81
## 1692          2188        10       0.03           64.84
## 1693          2191        10       0.03           64.87
## 1694          2200        10       0.03           64.90
## 1695          2225        10       0.03           64.93
## 1696          2243        10       0.03           64.96
## 1697          2262        10       0.03           64.99
## 1698          2295        10       0.03           65.02
## 1699          2300        10       0.03           65.05
## 1700          2314        10       0.03           65.08
## 1701          2320        10       0.03           65.11
## 1702          2327        10       0.03           65.14
## 1703          2339        10       0.03           65.17
## 1704          2341        10       0.03           65.20
## 1705          2345        10       0.03           65.23
## 1706          2361        10       0.03           65.26
## 1707          2401        10       0.03           65.29
## 1708          2402        10       0.03           65.32
## 1709          2407        10       0.03           65.35
## 1710          2420        10       0.03           65.38
## 1711          2439        10       0.03           65.41
## 1712          2476        10       0.03           65.44
## 1713          2479        10       0.03           65.47
## 1714          2489        10       0.03           65.50
## 1715          2521        10       0.03           65.53
## 1716          2543        10       0.03           65.56
## 1717          2548        10       0.03           65.59
## 1718          2556        10       0.03           65.62
## 1719          2562        10       0.03           65.65
## 1720          2564        10       0.03           65.68
## 1721          2585        10       0.03           65.71
## 1722          2590        10       0.03           65.74
## 1723          2636        10       0.03           65.77
## 1724          2656        10       0.03           65.80
## 1725          2691        10       0.03           65.83
## 1726          2692        10       0.03           65.86
## 1727          2699        10       0.03           65.89
## 1728          2713        10       0.03           65.92
## 1729          2723        10       0.03           65.95
## 1730          2727        10       0.03           65.98
## 1731          2732        10       0.03           66.01
## 1732          2754        10       0.03           66.04
## 1733          2756        10       0.03           66.07
## 1734          2757        10       0.03           66.10
## 1735          2763        10       0.03           66.13
## 1736          2775        10       0.03           66.16
## 1737          2777        10       0.03           66.19
## 1738          2785        10       0.03           66.22
## 1739          2806        10       0.03           66.25
## 1740          2817        10       0.03           66.28
## 1741          2825        10       0.03           66.31
## 1742          2829        10       0.03           66.34
## 1743          2834        10       0.03           66.37
## 1744          2864        10       0.03           66.40
## 1745          2883        10       0.03           66.43
## 1746          2904        10       0.03           66.46
## 1747          2927        10       0.03           66.49
## 1748          2935        10       0.03           66.52
## 1749          2948        10       0.03           66.55
## 1750          2958        10       0.03           66.58
## 1751          2972        10       0.03           66.61
## 1752          2979        10       0.03           66.64
## 1753          3015        10       0.03           66.67
## 1754          3021        10       0.03           66.70
## 1755          3030        10       0.03           66.73
## 1756          3034        10       0.03           66.76
## 1757          3039        10       0.03           66.79
## 1758          3063        10       0.03           66.82
## 1759          3067        10       0.03           66.85
## 1760          3083        10       0.03           66.88
## 1761          3127        10       0.03           66.91
## 1762          3132        10       0.03           66.94
## 1763          3160        10       0.03           66.97
## 1764          3186        10       0.03           67.00
## 1765          3215        10       0.03           67.03
## 1766          3222        10       0.03           67.06
## 1767          3224        10       0.03           67.09
## 1768          3236        10       0.03           67.12
## 1769          3254        10       0.03           67.15
## 1770          3264        10       0.03           67.18
## 1771          3295        10       0.03           67.21
## 1772          3298        10       0.03           67.24
## 1773          3304        10       0.03           67.27
## 1774          3343        10       0.03           67.30
## 1775          3382        10       0.03           67.33
## 1776          3384        10       0.03           67.36
## 1777          3401        10       0.03           67.39
## 1778          3413        10       0.03           67.42
## 1779          3419        10       0.03           67.45
## 1780          3435        10       0.03           67.48
## 1781          3458        10       0.03           67.51
## 1782          3471        10       0.03           67.54
## 1783          3475        10       0.03           67.57
## 1784          3496        10       0.03           67.60
## 1785          3522        10       0.03           67.63
## 1786          3526        10       0.03           67.66
## 1787          3544        10       0.03           67.69
## 1788          3556        10       0.03           67.72
## 1789          3609        10       0.03           67.75
## 1790          3614        10       0.03           67.78
## 1791          3615        10       0.03           67.81
## 1792          3619        10       0.03           67.84
## 1793          3622        10       0.03           67.87
## 1794          3660        10       0.03           67.90
## 1795          3671        10       0.03           67.93
## 1796          3681        10       0.03           67.96
## 1797          3685        10       0.03           67.99
## 1798          3689        10       0.03           68.02
## 1799          3717        10       0.03           68.05
## 1800          3721        10       0.03           68.08
## 1801          3738        10       0.03           68.11
## 1802          3756        10       0.03           68.14
## 1803          3808        10       0.03           68.17
## 1804          3819        10       0.03           68.20
## 1805          3840        10       0.03           68.23
## 1806          3866        10       0.03           68.26
## 1807          3886        10       0.03           68.29
## 1808          3895        10       0.03           68.32
## 1809          3919        10       0.03           68.35
## 1810          3928        10       0.03           68.38
## 1811          3937        10       0.03           68.41
## 1812          3947        10       0.03           68.44
## 1813          3961        10       0.03           68.47
## 1814          3997        10       0.03           68.50
## 1815          4004        10       0.03           68.53
## 1816          4028        10       0.03           68.56
## 1817          4037        10       0.03           68.59
## 1818          4044        10       0.03           68.62
## 1819          4085        10       0.03           68.65
## 1820          4088        10       0.03           68.68
## 1821          4092        10       0.03           68.71
## 1822          4094        10       0.03           68.74
## 1823          4096        10       0.03           68.77
## 1824          4105        10       0.03           68.80
## 1825          4114        10       0.03           68.83
## 1826          4164        10       0.03           68.86
## 1827          4177        10       0.03           68.89
## 1828          4195        10       0.03           68.92
## 1829          4196        10       0.03           68.95
## 1830          4204        10       0.03           68.98
## 1831          4244        10       0.03           69.01
## 1832          4265        10       0.03           69.04
## 1833          4269        10       0.03           69.07
## 1834          4284        10       0.03           69.10
## 1835          4296        10       0.03           69.13
## 1836          4313        10       0.03           69.16
## 1837          4342        10       0.03           69.19
## 1838          4369        10       0.03           69.22
## 1839          4398        10       0.03           69.25
## 1840          4405        10       0.03           69.28
## 1841          4432        10       0.03           69.31
## 1842          4449        10       0.03           69.34
## 1843          4457        10       0.03           69.37
## 1844          4463        10       0.03           69.40
## 1845          4466        10       0.03           69.43
## 1846          4493        10       0.03           69.46
## 1847          4500        10       0.03           69.49
## 1848          4529        10       0.03           69.52
## 1849          4541        10       0.03           69.55
## 1850          4559        10       0.03           69.58
## 1851          4583        10       0.03           69.61
## 1852          4584        10       0.03           69.64
## 1853          4593        10       0.03           69.67
## 1854          4596        10       0.03           69.70
## 1855          4603        10       0.03           69.73
## 1856          4614        10       0.03           69.76
## 1857          4629        10       0.03           69.79
## 1858          4632        10       0.03           69.82
## 1859          4641        10       0.03           69.85
## 1860          4655        10       0.03           69.88
## 1861          4669        10       0.03           69.91
## 1862          4675        10       0.03           69.94
## 1863          4684        10       0.03           69.97
## 1864          4687        10       0.03           70.00
## 1865          4705        10       0.03           70.03
## 1866          4712        10       0.03           70.06
## 1867          4722        10       0.03           70.09
## 1868          4725        10       0.03           70.12
## 1869          4727        10       0.03           70.15
## 1870          4728        10       0.03           70.18
## 1871          4740        10       0.03           70.21
## 1872          4772        10       0.03           70.24
## 1873          4782        10       0.03           70.27
## 1874          4793        10       0.03           70.30
## 1875          4837        10       0.03           70.33
## 1876          4840        10       0.03           70.36
## 1877          4855        10       0.03           70.39
## 1878          4869        10       0.03           70.42
## 1879          4883        10       0.03           70.45
## 1880          4886        10       0.03           70.48
## 1881          4899        10       0.03           70.51
## 1882          4911        10       0.03           70.54
## 1883          4914        10       0.03           70.57
## 1884          4922        10       0.03           70.60
## 1885          4942        10       0.03           70.63
## 1886          4981        10       0.03           70.66
## 1887          4989        10       0.03           70.69
## 1888          4991        10       0.03           70.72
## 1889          4993        10       0.03           70.75
## 1890          4996        10       0.03           70.78
## 1891          1009         9       0.02           70.80
## 1892          1027         9       0.02           70.82
## 1893          1034         9       0.02           70.84
## 1894          1045         9       0.02           70.86
## 1895          1054         9       0.02           70.88
## 1896          1088         9       0.02           70.90
## 1897          1126         9       0.02           70.92
## 1898          1139         9       0.02           70.94
## 1899          1141         9       0.02           70.96
## 1900          1154         9       0.02           70.98
## 1901          1163         9       0.02           71.00
## 1902          1165         9       0.02           71.02
## 1903          1168         9       0.02           71.04
## 1904          1173         9       0.02           71.06
## 1905          1186         9       0.02           71.08
## 1906          1194         9       0.02           71.10
## 1907          1209         9       0.02           71.12
## 1908          1215         9       0.02           71.14
## 1909          1268         9       0.02           71.16
## 1910          1281         9       0.02           71.18
## 1911          1297         9       0.02           71.20
## 1912          1306         9       0.02           71.22
## 1913          1319         9       0.02           71.24
## 1914          1325         9       0.02           71.26
## 1915          1331         9       0.02           71.28
## 1916          1336         9       0.02           71.30
## 1917          1399         9       0.02           71.32
## 1918          1431         9       0.02           71.34
## 1919          1449         9       0.02           71.36
## 1920          1495         9       0.02           71.38
## 1921          1497         9       0.02           71.40
## 1922          1503         9       0.02           71.42
## 1923          1544         9       0.02           71.44
## 1924          1546         9       0.02           71.46
## 1925          1549         9       0.02           71.48
## 1926          1617         9       0.02           71.50
## 1927          1624         9       0.02           71.52
## 1928          1627         9       0.02           71.54
## 1929          1655         9       0.02           71.56
## 1930          1669         9       0.02           71.58
## 1931          1670         9       0.02           71.60
## 1932          1698         9       0.02           71.62
## 1933          1742         9       0.02           71.64
## 1934          1756         9       0.02           71.66
## 1935          1773         9       0.02           71.68
## 1936          1779         9       0.02           71.70
## 1937          1799         9       0.02           71.72
## 1938          1803         9       0.02           71.74
## 1939          1804         9       0.02           71.76
## 1940          1824         9       0.02           71.78
## 1941          1828         9       0.02           71.80
## 1942          1829         9       0.02           71.82
## 1943          1843         9       0.02           71.84
## 1944          1847         9       0.02           71.86
## 1945          1853         9       0.02           71.88
## 1946          1874         9       0.02           71.90
## 1947          1928         9       0.02           71.92
## 1948          1947         9       0.02           71.94
## 1949          1970         9       0.02           71.96
## 1950          1987         9       0.02           71.98
## 1951          1993         9       0.02           72.00
## 1952          2020         9       0.02           72.02
## 1953          2044         9       0.02           72.04
## 1954          2049         9       0.02           72.06
## 1955          2059         9       0.02           72.08
## 1956          2067         9       0.02           72.10
## 1957          2073         9       0.02           72.12
## 1958          2104         9       0.02           72.14
## 1959          2141         9       0.02           72.16
## 1960          2147         9       0.02           72.18
## 1961          2149         9       0.02           72.20
## 1962          2156         9       0.02           72.22
## 1963          2167         9       0.02           72.24
## 1964          2233         9       0.02           72.26
## 1965          2237         9       0.02           72.28
## 1966          2241         9       0.02           72.30
## 1967          2256         9       0.02           72.32
## 1968          2266         9       0.02           72.34
## 1969          2301         9       0.02           72.36
## 1970          2312         9       0.02           72.38
## 1971          2326         9       0.02           72.40
## 1972          2343         9       0.02           72.42
## 1973          2353         9       0.02           72.44
## 1974          2358         9       0.02           72.46
## 1975          2416         9       0.02           72.48
## 1976          2419         9       0.02           72.50
## 1977          2427         9       0.02           72.52
## 1978          2446         9       0.02           72.54
## 1979          2460         9       0.02           72.56
## 1980          2466         9       0.02           72.58
## 1981          2471         9       0.02           72.60
## 1982          2500         9       0.02           72.62
## 1983          2508         9       0.02           72.64
## 1984          2544         9       0.02           72.66
## 1985          2561         9       0.02           72.68
## 1986          2623         9       0.02           72.70
## 1987          2649         9       0.02           72.72
## 1988          2700         9       0.02           72.74
## 1989          2702         9       0.02           72.76
## 1990          2703         9       0.02           72.78
## 1991          2742         9       0.02           72.80
## 1992          2762         9       0.02           72.82
## 1993          2778         9       0.02           72.84
## 1994          2782         9       0.02           72.86
## 1995          2788         9       0.02           72.88
## 1996          2804         9       0.02           72.90
## 1997          2824         9       0.02           72.92
## 1998          2831         9       0.02           72.94
## 1999          2843         9       0.02           72.96
## 2000          2850         9       0.02           72.98
## 2001          2888         9       0.02           73.00
## 2002          2914         9       0.02           73.02
## 2003          2921         9       0.02           73.04
## 2004          2928         9       0.02           73.06
## 2005          2934         9       0.02           73.08
## 2006          2962         9       0.02           73.10
## 2007          2974         9       0.02           73.12
## 2008          2981         9       0.02           73.14
## 2009          3022         9       0.02           73.16
## 2010          3023         9       0.02           73.18
## 2011          3027         9       0.02           73.20
## 2012          3053         9       0.02           73.22
## 2013          3059         9       0.02           73.24
## 2014          3079         9       0.02           73.26
## 2015          3109         9       0.02           73.28
## 2016          3123         9       0.02           73.30
## 2017          3158         9       0.02           73.32
## 2018          3161         9       0.02           73.34
## 2019          3241         9       0.02           73.36
## 2020          3256         9       0.02           73.38
## 2021          3259         9       0.02           73.40
## 2022          3267         9       0.02           73.42
## 2023          3273         9       0.02           73.44
## 2024          3283         9       0.02           73.46
## 2025          3312         9       0.02           73.48
## 2026          3334         9       0.02           73.50
## 2027          3338         9       0.02           73.52
## 2028          3339         9       0.02           73.54
## 2029          3357         9       0.02           73.56
## 2030          3378         9       0.02           73.58
## 2031          3407         9       0.02           73.60
## 2032          3427         9       0.02           73.62
## 2033          3459         9       0.02           73.64
## 2034          3470         9       0.02           73.66
## 2035          3525         9       0.02           73.68
## 2036          3551         9       0.02           73.70
## 2037          3573         9       0.02           73.72
## 2038          3639         9       0.02           73.74
## 2039          3646         9       0.02           73.76
## 2040          3656         9       0.02           73.78
## 2041          3658         9       0.02           73.80
## 2042          3667         9       0.02           73.82
## 2043          3670         9       0.02           73.84
## 2044          3680         9       0.02           73.86
## 2045          3686         9       0.02           73.88
## 2046          3699         9       0.02           73.90
## 2047          3716         9       0.02           73.92
## 2048          3731         9       0.02           73.94
## 2049          3735         9       0.02           73.96
## 2050          3749         9       0.02           73.98
## 2051          3751         9       0.02           74.00
## 2052          3759         9       0.02           74.02
## 2053          3765         9       0.02           74.04
## 2054          3766         9       0.02           74.06
## 2055          3767         9       0.02           74.08
## 2056          3784         9       0.02           74.10
## 2057          3785         9       0.02           74.12
## 2058          3787         9       0.02           74.14
## 2059          3801         9       0.02           74.16
## 2060          3804         9       0.02           74.18
## 2061          3809         9       0.02           74.20
## 2062          3815         9       0.02           74.22
## 2063          3816         9       0.02           74.24
## 2064          3828         9       0.02           74.26
## 2065          3829         9       0.02           74.28
## 2066          3839         9       0.02           74.30
## 2067          3842         9       0.02           74.32
## 2068          3843         9       0.02           74.34
## 2069          3861         9       0.02           74.36
## 2070          3890         9       0.02           74.38
## 2071          3898         9       0.02           74.40
## 2072          3907         9       0.02           74.42
## 2073          3927         9       0.02           74.44
## 2074          3929         9       0.02           74.46
## 2075          3952         9       0.02           74.48
## 2076          3953         9       0.02           74.50
## 2077          4003         9       0.02           74.52
## 2078          4008         9       0.02           74.54
## 2079          4013         9       0.02           74.56
## 2080          4046         9       0.02           74.58
## 2081          4048         9       0.02           74.60
## 2082          4050         9       0.02           74.62
## 2083          4059         9       0.02           74.64
## 2084          4063         9       0.02           74.66
## 2085          4071         9       0.02           74.68
## 2086          4074         9       0.02           74.70
## 2087          4103         9       0.02           74.72
## 2088          4119         9       0.02           74.74
## 2089          4122         9       0.02           74.76
## 2090          4132         9       0.02           74.78
## 2091          4149         9       0.02           74.80
## 2092          4172         9       0.02           74.82
## 2093          4179         9       0.02           74.84
## 2094          4226         9       0.02           74.86
## 2095          4230         9       0.02           74.88
## 2096          4245         9       0.02           74.90
## 2097          4252         9       0.02           74.92
## 2098          4264         9       0.02           74.94
## 2099          4289         9       0.02           74.96
## 2100          4298         9       0.02           74.98
## 2101          4325         9       0.02           75.00
## 2102          4337         9       0.02           75.02
## 2103          4344         9       0.02           75.04
## 2104          4355         9       0.02           75.06
## 2105          4356         9       0.02           75.08
## 2106          4357         9       0.02           75.10
## 2107          4359         9       0.02           75.12
## 2108          4371         9       0.02           75.14
## 2109          4394         9       0.02           75.16
## 2110          4401         9       0.02           75.18
## 2111          4408         9       0.02           75.20
## 2112          4461         9       0.02           75.22
## 2113          4471         9       0.02           75.24
## 2114          4478         9       0.02           75.26
## 2115          4479         9       0.02           75.28
## 2116          4492         9       0.02           75.30
## 2117          4502         9       0.02           75.32
## 2118          4539         9       0.02           75.34
## 2119          4554         9       0.02           75.36
## 2120          4556         9       0.02           75.38
## 2121          4561         9       0.02           75.40
## 2122          4578         9       0.02           75.42
## 2123          4582         9       0.02           75.44
## 2124          4591         9       0.02           75.46
## 2125          4617         9       0.02           75.48
## 2126          4620         9       0.02           75.50
## 2127          4634         9       0.02           75.52
## 2128          4640         9       0.02           75.54
## 2129          4648         9       0.02           75.56
## 2130          4680         9       0.02           75.58
## 2131          4690         9       0.02           75.60
## 2132          4710         9       0.02           75.62
## 2133          4733         9       0.02           75.64
## 2134          4749         9       0.02           75.66
## 2135          4758         9       0.02           75.68
## 2136          4847         9       0.02           75.70
## 2137          4879         9       0.02           75.72
## 2138          4944         9       0.02           75.74
## 2139          4950         9       0.02           75.76
## 2140          4960         9       0.02           75.78
## 2141          4977         9       0.02           75.80
## 2142          1002         8       0.02           75.82
## 2143          1003         8       0.02           75.84
## 2144          1018         8       0.02           75.86
## 2145          1021         8       0.02           75.88
## 2146          1043         8       0.02           75.90
## 2147          1049         8       0.02           75.92
## 2148          1057         8       0.02           75.94
## 2149          1058         8       0.02           75.96
## 2150          1067         8       0.02           75.98
## 2151          1095         8       0.02           76.00
## 2152          1115         8       0.02           76.02
## 2153          1140         8       0.02           76.04
## 2154          1142         8       0.02           76.06
## 2155          1152         8       0.02           76.08
## 2156          1155         8       0.02           76.10
## 2157          1181         8       0.02           76.12
## 2158          1188         8       0.02           76.14
## 2159          1196         8       0.02           76.16
## 2160          1200         8       0.02           76.18
## 2161          1207         8       0.02           76.20
## 2162          1212         8       0.02           76.22
## 2163          1217         8       0.02           76.24
## 2164          1229         8       0.02           76.26
## 2165          1244         8       0.02           76.28
## 2166          1246         8       0.02           76.30
## 2167          1261         8       0.02           76.32
## 2168          1280         8       0.02           76.34
## 2169          1295         8       0.02           76.36
## 2170          1299         8       0.02           76.38
## 2171          1308         8       0.02           76.40
## 2172          1311         8       0.02           76.42
## 2173          1323         8       0.02           76.44
## 2174          1364         8       0.02           76.46
## 2175          1369         8       0.02           76.48
## 2176          1389         8       0.02           76.50
## 2177          1396         8       0.02           76.52
## 2178          1398         8       0.02           76.54
## 2179          1434         8       0.02           76.56
## 2180          1446         8       0.02           76.58
## 2181          1461         8       0.02           76.60
## 2182          1478         8       0.02           76.62
## 2183          1484         8       0.02           76.64
## 2184          1488         8       0.02           76.66
## 2185          1498         8       0.02           76.68
## 2186          1505         8       0.02           76.70
## 2187          1508         8       0.02           76.72
## 2188          1528         8       0.02           76.74
## 2189          1535         8       0.02           76.76
## 2190          1536         8       0.02           76.78
## 2191          1564         8       0.02           76.80
## 2192          1569         8       0.02           76.82
## 2193          1571         8       0.02           76.84
## 2194          1578         8       0.02           76.86
## 2195          1585         8       0.02           76.88
## 2196          1588         8       0.02           76.90
## 2197          1597         8       0.02           76.92
## 2198          1604         8       0.02           76.94
## 2199          1606         8       0.02           76.96
## 2200          1638         8       0.02           76.98
## 2201          1678         8       0.02           77.00
## 2202          1684         8       0.02           77.02
## 2203          1685         8       0.02           77.04
## 2204          1705         8       0.02           77.06
## 2205          1716         8       0.02           77.08
## 2206          1717         8       0.02           77.10
## 2207          1730         8       0.02           77.12
## 2208          1738         8       0.02           77.14
## 2209          1749         8       0.02           77.16
## 2210          1760         8       0.02           77.18
## 2211          1765         8       0.02           77.20
## 2212          1772         8       0.02           77.22
## 2213          1791         8       0.02           77.24
## 2214          1821         8       0.02           77.26
## 2215          1848         8       0.02           77.28
## 2216          1849         8       0.02           77.30
## 2217          1850         8       0.02           77.32
## 2218          1856         8       0.02           77.34
## 2219          1864         8       0.02           77.36
## 2220          1879         8       0.02           77.38
## 2221          1890         8       0.02           77.40
## 2222          1893         8       0.02           77.42
## 2223          1897         8       0.02           77.44
## 2224          1955         8       0.02           77.46
## 2225          1971         8       0.02           77.48
## 2226          1985         8       0.02           77.50
## 2227          1992         8       0.02           77.52
## 2228          2025         8       0.02           77.54
## 2229          2037         8       0.02           77.56
## 2230          2053         8       0.02           77.58
## 2231          2062         8       0.02           77.60
## 2232          2064         8       0.02           77.62
## 2233          2076         8       0.02           77.64
## 2234          2085         8       0.02           77.66
## 2235          2110         8       0.02           77.68
## 2236          2111         8       0.02           77.70
## 2237          2113         8       0.02           77.72
## 2238          2119         8       0.02           77.74
## 2239          2135         8       0.02           77.76
## 2240          2155         8       0.02           77.78
## 2241          2159         8       0.02           77.80
## 2242          2195         8       0.02           77.82
## 2243          2205         8       0.02           77.84
## 2244          2207         8       0.02           77.86
## 2245          2208         8       0.02           77.88
## 2246          2217         8       0.02           77.90
## 2247          2245         8       0.02           77.92
## 2248          2250         8       0.02           77.94
## 2249          2257         8       0.02           77.96
## 2250          2260         8       0.02           77.98
## 2251          2264         8       0.02           78.00
## 2252          2279         8       0.02           78.02
## 2253          2287         8       0.02           78.04
## 2254          2299         8       0.02           78.06
## 2255          2368         8       0.02           78.08
## 2256          2369         8       0.02           78.10
## 2257          2376         8       0.02           78.12
## 2258          2388         8       0.02           78.14
## 2259          2444         8       0.02           78.16
## 2260          2445         8       0.02           78.18
## 2261          2449         8       0.02           78.20
## 2262          2464         8       0.02           78.22
## 2263          2468         8       0.02           78.24
## 2264          2472         8       0.02           78.26
## 2265          2483         8       0.02           78.28
## 2266          2496         8       0.02           78.30
## 2267          2506         8       0.02           78.32
## 2268          2509         8       0.02           78.34
## 2269          2516         8       0.02           78.36
## 2270          2522         8       0.02           78.38
## 2271          2537         8       0.02           78.40
## 2272          2542         8       0.02           78.42
## 2273          2571         8       0.02           78.44
## 2274          2577         8       0.02           78.46
## 2275          2594         8       0.02           78.48
## 2276          2606         8       0.02           78.50
## 2277          2608         8       0.02           78.52
## 2278          2616         8       0.02           78.54
## 2279          2620         8       0.02           78.56
## 2280          2627         8       0.02           78.58
## 2281          2639         8       0.02           78.60
## 2282          2661         8       0.02           78.62
## 2283          2664         8       0.02           78.64
## 2284          2671         8       0.02           78.66
## 2285          2673         8       0.02           78.68
## 2286          2680         8       0.02           78.70
## 2287          2683         8       0.02           78.72
## 2288          2695         8       0.02           78.74
## 2289          2698         8       0.02           78.76
## 2290          2726         8       0.02           78.78
## 2291          2744         8       0.02           78.80
## 2292          2750         8       0.02           78.82
## 2293          2753         8       0.02           78.84
## 2294          2790         8       0.02           78.86
## 2295          2798         8       0.02           78.88
## 2296          2801         8       0.02           78.90
## 2297          2802         8       0.02           78.92
## 2298          2815         8       0.02           78.94
## 2299          2827         8       0.02           78.96
## 2300          2839         8       0.02           78.98
## 2301          2865         8       0.02           79.00
## 2302          2871         8       0.02           79.02
## 2303          2872         8       0.02           79.04
## 2304          2880         8       0.02           79.06
## 2305          2884         8       0.02           79.08
## 2306          2901         8       0.02           79.10
## 2307          2908         8       0.02           79.12
## 2308          2933         8       0.02           79.14
## 2309          2939         8       0.02           79.16
## 2310          2943         8       0.02           79.18
## 2311          2969         8       0.02           79.20
## 2312          2999         8       0.02           79.22
## 2313          3020         8       0.02           79.24
## 2314          3033         8       0.02           79.26
## 2315          3058         8       0.02           79.28
## 2316          3061         8       0.02           79.30
## 2317          3088         8       0.02           79.32
## 2318          3102         8       0.02           79.34
## 2319          3106         8       0.02           79.36
## 2320          3112         8       0.02           79.38
## 2321          3133         8       0.02           79.40
## 2322          3145         8       0.02           79.42
## 2323          3200         8       0.02           79.44
## 2324          3210         8       0.02           79.46
## 2325          3226         8       0.02           79.48
## 2326          3228         8       0.02           79.50
## 2327          3238         8       0.02           79.52
## 2328          3242         8       0.02           79.54
## 2329          3260         8       0.02           79.56
## 2330          3275         8       0.02           79.58
## 2331          3303         8       0.02           79.60
## 2332          3311         8       0.02           79.62
## 2333          3331         8       0.02           79.64
## 2334          3342         8       0.02           79.66
## 2335          3349         8       0.02           79.68
## 2336          3386         8       0.02           79.70
## 2337          3411         8       0.02           79.72
## 2338          3417         8       0.02           79.74
## 2339          3423         8       0.02           79.76
## 2340          3426         8       0.02           79.78
## 2341          3428         8       0.02           79.80
## 2342          3443         8       0.02           79.82
## 2343          3444         8       0.02           79.84
## 2344          3449         8       0.02           79.86
## 2345          3451         8       0.02           79.88
## 2346          3452         8       0.02           79.90
## 2347          3455         8       0.02           79.92
## 2348          3463         8       0.02           79.94
## 2349          3479         8       0.02           79.96
## 2350          3493         8       0.02           79.98
## 2351          3498         8       0.02           80.00
## 2352          3521         8       0.02           80.02
## 2353          3546         8       0.02           80.04
## 2354          3550         8       0.02           80.06
## 2355          3554         8       0.02           80.08
## 2356          3561         8       0.02           80.10
## 2357          3563         8       0.02           80.12
## 2358          3564         8       0.02           80.14
## 2359          3568         8       0.02           80.16
## 2360          3586         8       0.02           80.18
## 2361          3591         8       0.02           80.20
## 2362          3601         8       0.02           80.22
## 2363          3636         8       0.02           80.24
## 2364          3640         8       0.02           80.26
## 2365          3659         8       0.02           80.28
## 2366          3662         8       0.02           80.30
## 2367          3664         8       0.02           80.32
## 2368          3665         8       0.02           80.34
## 2369          3673         8       0.02           80.36
## 2370          3693         8       0.02           80.38
## 2371          3695         8       0.02           80.40
## 2372          3710         8       0.02           80.42
## 2373          3712         8       0.02           80.44
## 2374          3713         8       0.02           80.46
## 2375          3720         8       0.02           80.48
## 2376          3729         8       0.02           80.50
## 2377          3730         8       0.02           80.52
## 2378          3772         8       0.02           80.54
## 2379          3773         8       0.02           80.56
## 2380          3795         8       0.02           80.58
## 2381          3850         8       0.02           80.60
## 2382          3851         8       0.02           80.62
## 2383          3854         8       0.02           80.64
## 2384          3867         8       0.02           80.66
## 2385          3869         8       0.02           80.68
## 2386          3904         8       0.02           80.70
## 2387          3921         8       0.02           80.72
## 2388          3923         8       0.02           80.74
## 2389          3925         8       0.02           80.76
## 2390          3930         8       0.02           80.78
## 2391          3935         8       0.02           80.80
## 2392          3965         8       0.02           80.82
## 2393          4001         8       0.02           80.84
## 2394          4014         8       0.02           80.86
## 2395          4017         8       0.02           80.88
## 2396          4022         8       0.02           80.90
## 2397          4066         8       0.02           80.92
## 2398          4075         8       0.02           80.94
## 2399          4080         8       0.02           80.96
## 2400          4100         8       0.02           80.98
## 2401          4101         8       0.02           81.00
## 2402          4116         8       0.02           81.02
## 2403          4144         8       0.02           81.04
## 2404          4154         8       0.02           81.06
## 2405          4171         8       0.02           81.08
## 2406          4184         8       0.02           81.10
## 2407          4193         8       0.02           81.12
## 2408          4213         8       0.02           81.14
## 2409          4219         8       0.02           81.16
## 2410          4221         8       0.02           81.18
## 2411          4229         8       0.02           81.20
## 2412          4238         8       0.02           81.22
## 2413          4246         8       0.02           81.24
## 2414          4273         8       0.02           81.26
## 2415          4285         8       0.02           81.28
## 2416          4300         8       0.02           81.30
## 2417          4304         8       0.02           81.32
## 2418          4349         8       0.02           81.34
## 2419          4361         8       0.02           81.36
## 2420          4368         8       0.02           81.38
## 2421          4370         8       0.02           81.40
## 2422          4395         8       0.02           81.42
## 2423          4415         8       0.02           81.44
## 2424          4418         8       0.02           81.46
## 2425          4424         8       0.02           81.48
## 2426          4435         8       0.02           81.50
## 2427          4439         8       0.02           81.52
## 2428          4460         8       0.02           81.54
## 2429          4489         8       0.02           81.56
## 2430          4522         8       0.02           81.58
## 2431          4538         8       0.02           81.60
## 2432          4552         8       0.02           81.62
## 2433          4557         8       0.02           81.64
## 2434          4575         8       0.02           81.66
## 2435          4580         8       0.02           81.68
## 2436          4607         8       0.02           81.70
## 2437          4622         8       0.02           81.72
## 2438          4635         8       0.02           81.74
## 2439          4638         8       0.02           81.76
## 2440          4651         8       0.02           81.78
## 2441          4658         8       0.02           81.80
## 2442          4659         8       0.02           81.82
## 2443          4660         8       0.02           81.84
## 2444          4664         8       0.02           81.86
## 2445          4665         8       0.02           81.88
## 2446          4691         8       0.02           81.90
## 2447          4698         8       0.02           81.92
## 2448          4701         8       0.02           81.94
## 2449          4711         8       0.02           81.96
## 2450          4726         8       0.02           81.98
## 2451          4752         8       0.02           82.00
## 2452          4763         8       0.02           82.02
## 2453          4764         8       0.02           82.04
## 2454          4765         8       0.02           82.06
## 2455          4798         8       0.02           82.08
## 2456          4818         8       0.02           82.10
## 2457          4823         8       0.02           82.12
## 2458          4830         8       0.02           82.14
## 2459          4838         8       0.02           82.16
## 2460          4839         8       0.02           82.18
## 2461          4845         8       0.02           82.20
## 2462          4854         8       0.02           82.22
## 2463          4856         8       0.02           82.24
## 2464          4859         8       0.02           82.26
## 2465          4873         8       0.02           82.28
## 2466          4876         8       0.02           82.30
## 2467          4881         8       0.02           82.32
## 2468          4893         8       0.02           82.34
## 2469          4894         8       0.02           82.36
## 2470          4896         8       0.02           82.38
## 2471          4897         8       0.02           82.40
## 2472          4901         8       0.02           82.42
## 2473          4903         8       0.02           82.44
## 2474          4919         8       0.02           82.46
## 2475          4934         8       0.02           82.48
## 2476          4935         8       0.02           82.50
## 2477          4940         8       0.02           82.52
## 2478          4954         8       0.02           82.54
## 2479          4956         8       0.02           82.56
## 2480          4963         8       0.02           82.58
## 2481          4985         8       0.02           82.60
## 2482          4990         8       0.02           82.62
## 2483          1015         7       0.02           82.64
## 2484          1031         7       0.02           82.66
## 2485          1064         7       0.02           82.68
## 2486          1078         7       0.02           82.70
## 2487          1083         7       0.02           82.72
## 2488          1085         7       0.02           82.74
## 2489          1101         7       0.02           82.76
## 2490          1134         7       0.02           82.78
## 2491          1149         7       0.02           82.80
## 2492          1157         7       0.02           82.82
## 2493          1161         7       0.02           82.84
## 2494          1187         7       0.02           82.86
## 2495          1198         7       0.02           82.88
## 2496          1232         7       0.02           82.90
## 2497          1274         7       0.02           82.92
## 2498          1288         7       0.02           82.94
## 2499          1298         7       0.02           82.96
## 2500          1301         7       0.02           82.98
## 2501          1304         7       0.02           83.00
## 2502          1346         7       0.02           83.02
## 2503          1376         7       0.02           83.04
## 2504          1388         7       0.02           83.06
## 2505          1393         7       0.02           83.08
## 2506          1408         7       0.02           83.10
## 2507          1413         7       0.02           83.12
## 2508          1418         7       0.02           83.14
## 2509          1458         7       0.02           83.16
## 2510          1487         7       0.02           83.18
## 2511          1502         7       0.02           83.20
## 2512          1518         7       0.02           83.22
## 2513          1529         7       0.02           83.24
## 2514          1545         7       0.02           83.26
## 2515          1547         7       0.02           83.28
## 2516          1550         7       0.02           83.30
## 2517          1559         7       0.02           83.32
## 2518          1593         7       0.02           83.34
## 2519          1598         7       0.02           83.36
## 2520          1639         7       0.02           83.38
## 2521          1647         7       0.02           83.40
## 2522          1660         7       0.02           83.42
## 2523          1686         7       0.02           83.44
## 2524          1718         7       0.02           83.46
## 2525          1720         7       0.02           83.48
## 2526          1728         7       0.02           83.50
## 2527          1732         7       0.02           83.52
## 2528          1763         7       0.02           83.54
## 2529          1784         7       0.02           83.56
## 2530          1805         7       0.02           83.58
## 2531          1831         7       0.02           83.60
## 2532          1834         7       0.02           83.62
## 2533          1845         7       0.02           83.64
## 2534          1868         7       0.02           83.66
## 2535          1902         7       0.02           83.68
## 2536          1909         7       0.02           83.70
## 2537          1911         7       0.02           83.72
## 2538          1914         7       0.02           83.74
## 2539          1916         7       0.02           83.76
## 2540          1958         7       0.02           83.78
## 2541          1982         7       0.02           83.80
## 2542          2000         7       0.02           83.82
## 2543          2002         7       0.02           83.84
## 2544          2013         7       0.02           83.86
## 2545          2023         7       0.02           83.88
## 2546          2030         7       0.02           83.90
## 2547          2032         7       0.02           83.92
## 2548          2098         7       0.02           83.94
## 2549          2108         7       0.02           83.96
## 2550          2115         7       0.02           83.98
## 2551          2134         7       0.02           84.00
## 2552          2143         7       0.02           84.02
## 2553          2168         7       0.02           84.04
## 2554          2174         7       0.02           84.06
## 2555          2181         7       0.02           84.08
## 2556          2183         7       0.02           84.10
## 2557          2206         7       0.02           84.12
## 2558          2258         7       0.02           84.14
## 2559          2259         7       0.02           84.16
## 2560          2276         7       0.02           84.18
## 2561          2277         7       0.02           84.20
## 2562          2283         7       0.02           84.22
## 2563          2305         7       0.02           84.24
## 2564          2319         7       0.02           84.26
## 2565          2328         7       0.02           84.28
## 2566          2392         7       0.02           84.30
## 2567          2398         7       0.02           84.32
## 2568          2412         7       0.02           84.34
## 2569          2434         7       0.02           84.36
## 2570          2451         7       0.02           84.38
## 2571          2477         7       0.02           84.40
## 2572          2485         7       0.02           84.42
## 2573          2488         7       0.02           84.44
## 2574          2528         7       0.02           84.46
## 2575          2533         7       0.02           84.48
## 2576          2536         7       0.02           84.50
## 2577          2538         7       0.02           84.52
## 2578          2569         7       0.02           84.54
## 2579          2610         7       0.02           84.56
## 2580          2611         7       0.02           84.58
## 2581          2619         7       0.02           84.60
## 2582          2626         7       0.02           84.62
## 2583          2630         7       0.02           84.64
## 2584          2631         7       0.02           84.66
## 2585          2642         7       0.02           84.68
## 2586          2644         7       0.02           84.70
## 2587          2646         7       0.02           84.72
## 2588          2658         7       0.02           84.74
## 2589          2675         7       0.02           84.76
## 2590          2749         7       0.02           84.78
## 2591          2766         7       0.02           84.80
## 2592          2768         7       0.02           84.82
## 2593          2771         7       0.02           84.84
## 2594          2774         7       0.02           84.86
## 2595          2786         7       0.02           84.88
## 2596          2838         7       0.02           84.90
## 2597          2863         7       0.02           84.92
## 2598          2875         7       0.02           84.94
## 2599          2898         7       0.02           84.96
## 2600          2902         7       0.02           84.98
## 2601          2926         7       0.02           85.00
## 2602          2938         7       0.02           85.02
## 2603          2947         7       0.02           85.04
## 2604          2951         7       0.02           85.06
## 2605          2954         7       0.02           85.08
## 2606          2970         7       0.02           85.10
## 2607          2971         7       0.02           85.12
## 2608          2980         7       0.02           85.14
## 2609          3006         7       0.02           85.16
## 2610          3016         7       0.02           85.18
## 2611          3055         7       0.02           85.20
## 2612          3060         7       0.02           85.22
## 2613          3065         7       0.02           85.24
## 2614          3068         7       0.02           85.26
## 2615          3096         7       0.02           85.28
## 2616          3118         7       0.02           85.30
## 2617          3157         7       0.02           85.32
## 2618          3159         7       0.02           85.34
## 2619          3167         7       0.02           85.36
## 2620          3172         7       0.02           85.38
## 2621          3183         7       0.02           85.40
## 2622          3202         7       0.02           85.42
## 2623          3213         7       0.02           85.44
## 2624          3219         7       0.02           85.46
## 2625          3235         7       0.02           85.48
## 2626          3263         7       0.02           85.50
## 2627          3265         7       0.02           85.52
## 2628          3271         7       0.02           85.54
## 2629          3277         7       0.02           85.56
## 2630          3279         7       0.02           85.58
## 2631          3285         7       0.02           85.60
## 2632          3293         7       0.02           85.62
## 2633          3316         7       0.02           85.64
## 2634          3317         7       0.02           85.66
## 2635          3352         7       0.02           85.68
## 2636          3375         7       0.02           85.70
## 2637          3387         7       0.02           85.72
## 2638          3394         7       0.02           85.74
## 2639          3403         7       0.02           85.76
## 2640          3433         7       0.02           85.78
## 2641          3466         7       0.02           85.80
## 2642          3482         7       0.02           85.82
## 2643          3488         7       0.02           85.84
## 2644          3494         7       0.02           85.86
## 2645          3513         7       0.02           85.88
## 2646          3516         7       0.02           85.90
## 2647          3540         7       0.02           85.92
## 2648          3577         7       0.02           85.94
## 2649          3611         7       0.02           85.96
## 2650          3616         7       0.02           85.98
## 2651          3644         7       0.02           86.00
## 2652          3708         7       0.02           86.02
## 2653          3715         7       0.02           86.04
## 2654          3739         7       0.02           86.06
## 2655          3781         7       0.02           86.08
## 2656          3806         7       0.02           86.10
## 2657          3852         7       0.02           86.12
## 2658          3860         7       0.02           86.14
## 2659          3871         7       0.02           86.16
## 2660          3902         7       0.02           86.18
## 2661          3912         7       0.02           86.20
## 2662          3954         7       0.02           86.22
## 2663          4031         7       0.02           86.24
## 2664          4058         7       0.02           86.26
## 2665          4060         7       0.02           86.28
## 2666          4126         7       0.02           86.30
## 2667          4175         7       0.02           86.32
## 2668          4176         7       0.02           86.34
## 2669          4227         7       0.02           86.36
## 2670          4242         7       0.02           86.38
## 2671          4283         7       0.02           86.40
## 2672          4290         7       0.02           86.42
## 2673          4310         7       0.02           86.44
## 2674          4315         7       0.02           86.46
## 2675          4329         7       0.02           86.48
## 2676          4341         7       0.02           86.50
## 2677          4343         7       0.02           86.52
## 2678          4373         7       0.02           86.54
## 2679          4404         7       0.02           86.56
## 2680          4409         7       0.02           86.58
## 2681          4413         7       0.02           86.60
## 2682          4414         7       0.02           86.62
## 2683          4443         7       0.02           86.64
## 2684          4450         7       0.02           86.66
## 2685          4469         7       0.02           86.68
## 2686          4477         7       0.02           86.70
## 2687          4511         7       0.02           86.72
## 2688          4516         7       0.02           86.74
## 2689          4535         7       0.02           86.76
## 2690          4547         7       0.02           86.78
## 2691          4553         7       0.02           86.80
## 2692          4586         7       0.02           86.82
## 2693          4626         7       0.02           86.84
## 2694          4654         7       0.02           86.86
## 2695          4670         7       0.02           86.88
## 2696          4672         7       0.02           86.90
## 2697          4673         7       0.02           86.92
## 2698          4677         7       0.02           86.94
## 2699          4689         7       0.02           86.96
## 2700          4696         7       0.02           86.98
## 2701          4702         7       0.02           87.00
## 2702          4770         7       0.02           87.02
## 2703          4771         7       0.02           87.04
## 2704          4786         7       0.02           87.06
## 2705          4811         7       0.02           87.08
## 2706          4813         7       0.02           87.10
## 2707          4833         7       0.02           87.12
## 2708          4849         7       0.02           87.14
## 2709          4871         7       0.02           87.16
## 2710          4878         7       0.02           87.18
## 2711          4908         7       0.02           87.20
## 2712          4913         7       0.02           87.22
## 2713          4968         7       0.02           87.24
## 2714          4970         7       0.02           87.26
## 2715          4976         7       0.02           87.28
## 2716          4979         7       0.02           87.30
## 2717          4984         7       0.02           87.32
## 2718          4987         7       0.02           87.34
## 2719          5000         7       0.02           87.36
## 2720          1022         6       0.02           87.38
## 2721          1025         6       0.02           87.40
## 2722          1042         6       0.02           87.42
## 2723          1047         6       0.02           87.44
## 2724          1048         6       0.02           87.46
## 2725          1055         6       0.02           87.48
## 2726          1056         6       0.02           87.50
## 2727          1066         6       0.02           87.52
## 2728          1079         6       0.02           87.54
## 2729          1099         6       0.02           87.56
## 2730          1105         6       0.02           87.58
## 2731          1122         6       0.02           87.60
## 2732          1137         6       0.02           87.62
## 2733          1138         6       0.02           87.64
## 2734          1145         6       0.02           87.66
## 2735          1147         6       0.02           87.68
## 2736          1159         6       0.02           87.70
## 2737          1191         6       0.02           87.72
## 2738          1195         6       0.02           87.74
## 2739          1214         6       0.02           87.76
## 2740          1253         6       0.02           87.78
## 2741          1258         6       0.02           87.80
## 2742          1262         6       0.02           87.82
## 2743          1270         6       0.02           87.84
## 2744          1315         6       0.02           87.86
## 2745          1316         6       0.02           87.88
## 2746          1317         6       0.02           87.90
## 2747          1344         6       0.02           87.92
## 2748          1348         6       0.02           87.94
## 2749          1350         6       0.02           87.96
## 2750          1351         6       0.02           87.98
## 2751          1357         6       0.02           88.00
## 2752          1371         6       0.02           88.02
## 2753          1382         6       0.02           88.04
## 2754          1383         6       0.02           88.06
## 2755          1386         6       0.02           88.08
## 2756          1387         6       0.02           88.10
## 2757          1392         6       0.02           88.12
## 2758          1405         6       0.02           88.14
## 2759          1409         6       0.02           88.16
## 2760          1423         6       0.02           88.18
## 2761          1424         6       0.02           88.20
## 2762          1445         6       0.02           88.22
## 2763          1451         6       0.02           88.24
## 2764          1463         6       0.02           88.26
## 2765          1520         6       0.02           88.28
## 2766          1521         6       0.02           88.30
## 2767          1532         6       0.02           88.32
## 2768          1533         6       0.02           88.34
## 2769          1538         6       0.02           88.36
## 2770          1548         6       0.02           88.38
## 2771          1562         6       0.02           88.40
## 2772          1573         6       0.02           88.42
## 2773          1581         6       0.02           88.44
## 2774          1582         6       0.02           88.46
## 2775          1586         6       0.02           88.48
## 2776          1590         6       0.02           88.50
## 2777          1594         6       0.02           88.52
## 2778          1601         6       0.02           88.54
## 2779          1607         6       0.02           88.56
## 2780          1610         6       0.02           88.58
## 2781          1629         6       0.02           88.60
## 2782          1633         6       0.02           88.62
## 2783          1635         6       0.02           88.64
## 2784          1650         6       0.02           88.66
## 2785          1657         6       0.02           88.68
## 2786          1665         6       0.02           88.70
## 2787          1672         6       0.02           88.72
## 2788          1680         6       0.02           88.74
## 2789          1681         6       0.02           88.76
## 2790          1694         6       0.02           88.78
## 2791          1710         6       0.02           88.80
## 2792          1721         6       0.02           88.82
## 2793          1725         6       0.02           88.84
## 2794          1727         6       0.02           88.86
## 2795          1771         6       0.02           88.88
## 2796          1778         6       0.02           88.90
## 2797          1781         6       0.02           88.92
## 2798          1786         6       0.02           88.94
## 2799          1807         6       0.02           88.96
## 2800          1809         6       0.02           88.98
## 2801          1836         6       0.02           89.00
## 2802          1842         6       0.02           89.02
## 2803          1854         6       0.02           89.04
## 2804          1873         6       0.02           89.06
## 2805          1882         6       0.02           89.08
## 2806          1891         6       0.02           89.10
## 2807          1904         6       0.02           89.12
## 2808          1912         6       0.02           89.14
## 2809          1920         6       0.02           89.16
## 2810          1926         6       0.02           89.18
## 2811          1927         6       0.02           89.20
## 2812          1936         6       0.02           89.22
## 2813          1951         6       0.02           89.24
## 2814          1978         6       0.02           89.26
## 2815          1988         6       0.02           89.28
## 2816          1990         6       0.02           89.30
## 2817          2003         6       0.02           89.32
## 2818          2007         6       0.02           89.34
## 2819          2008         6       0.02           89.36
## 2820          2009         6       0.02           89.38
## 2821          2034         6       0.02           89.40
## 2822          2036         6       0.02           89.42
## 2823          2075         6       0.02           89.44
## 2824          2078         6       0.02           89.46
## 2825          2094         6       0.02           89.48
## 2826          2095         6       0.02           89.50
## 2827          2114         6       0.02           89.52
## 2828          2125         6       0.02           89.54
## 2829          2140         6       0.02           89.56
## 2830          2146         6       0.02           89.58
## 2831          2177         6       0.02           89.60
## 2832          2187         6       0.02           89.62
## 2833          2190         6       0.02           89.64
## 2834          2219         6       0.02           89.66
## 2835          2220         6       0.02           89.68
## 2836          2221         6       0.02           89.70
## 2837          2253         6       0.02           89.72
## 2838          2269         6       0.02           89.74
## 2839          2278         6       0.02           89.76
## 2840          2286         6       0.02           89.78
## 2841          2303         6       0.02           89.80
## 2842          2308         6       0.02           89.82
## 2843          2316         6       0.02           89.84
## 2844          2318         6       0.02           89.86
## 2845          2323         6       0.02           89.88
## 2846          2324         6       0.02           89.90
## 2847          2351         6       0.02           89.92
## 2848          2352         6       0.02           89.94
## 2849          2354         6       0.02           89.96
## 2850          2360         6       0.02           89.98
## 2851          2371         6       0.02           90.00
## 2852          2372         6       0.02           90.02
## 2853          2379         6       0.02           90.04
## 2854          2384         6       0.02           90.06
## 2855          2397         6       0.02           90.08
## 2856          2411         6       0.02           90.10
## 2857          2424         6       0.02           90.12
## 2858          2450         6       0.02           90.14
## 2859          2457         6       0.02           90.16
## 2860          2458         6       0.02           90.18
## 2861          2463         6       0.02           90.20
## 2862          2473         6       0.02           90.22
## 2863          2481         6       0.02           90.24
## 2864          2490         6       0.02           90.26
## 2865          2520         6       0.02           90.28
## 2866          2541         6       0.02           90.30
## 2867          2551         6       0.02           90.32
## 2868          2557         6       0.02           90.34
## 2869          2559         6       0.02           90.36
## 2870          2579         6       0.02           90.38
## 2871          2593         6       0.02           90.40
## 2872          2605         6       0.02           90.42
## 2873          2635         6       0.02           90.44
## 2874          2657         6       0.02           90.46
## 2875          2662         6       0.02           90.48
## 2876          2670         6       0.02           90.50
## 2877          2674         6       0.02           90.52
## 2878          2677         6       0.02           90.54
## 2879          2679         6       0.02           90.56
## 2880          2681         6       0.02           90.58
## 2881          2704         6       0.02           90.60
## 2882          2705         6       0.02           90.62
## 2883          2708         6       0.02           90.64
## 2884          2721         6       0.02           90.66
## 2885          2724         6       0.02           90.68
## 2886          2733         6       0.02           90.70
## 2887          2737         6       0.02           90.72
## 2888          2780         6       0.02           90.74
## 2889          2808         6       0.02           90.76
## 2890          2809         6       0.02           90.78
## 2891          2818         6       0.02           90.80
## 2892          2846         6       0.02           90.82
## 2893          2862         6       0.02           90.84
## 2894          2877         6       0.02           90.86
## 2895          2890         6       0.02           90.88
## 2896          2897         6       0.02           90.90
## 2897          2905         6       0.02           90.92
## 2898          2917         6       0.02           90.94
## 2899          2922         6       0.02           90.96
## 2900          2965         6       0.02           90.98
## 2901          2966         6       0.02           91.00
## 2902          2967         6       0.02           91.02
## 2903          2985         6       0.02           91.04
## 2904          2994         6       0.02           91.06
## 2905          3003         6       0.02           91.08
## 2906          3012         6       0.02           91.10
## 2907          3017         6       0.02           91.12
## 2908          3018         6       0.02           91.14
## 2909          3029         6       0.02           91.16
## 2910          3069         6       0.02           91.18
## 2911          3075         6       0.02           91.20
## 2912          3087         6       0.02           91.22
## 2913          3092         6       0.02           91.24
## 2914          3110         6       0.02           91.26
## 2915          3129         6       0.02           91.28
## 2916          3130         6       0.02           91.30
## 2917          3135         6       0.02           91.32
## 2918          3143         6       0.02           91.34
## 2919          3150         6       0.02           91.36
## 2920          3151         6       0.02           91.38
## 2921          3156         6       0.02           91.40
## 2922          3169         6       0.02           91.42
## 2923          3188         6       0.02           91.44
## 2924          3195         6       0.02           91.46
## 2925          3217         6       0.02           91.48
## 2926          3244         6       0.02           91.50
## 2927          3280         6       0.02           91.52
## 2928          3281         6       0.02           91.54
## 2929          3288         6       0.02           91.56
## 2930          3292         6       0.02           91.58
## 2931          3302         6       0.02           91.60
## 2932          3305         6       0.02           91.62
## 2933          3313         6       0.02           91.64
## 2934          3320         6       0.02           91.66
## 2935          3346         6       0.02           91.68
## 2936          3351         6       0.02           91.70
## 2937          3355         6       0.02           91.72
## 2938          3368         6       0.02           91.74
## 2939          3383         6       0.02           91.76
## 2940          3397         6       0.02           91.78
## 2941          3406         6       0.02           91.80
## 2942          3408         6       0.02           91.82
## 2943          3415         6       0.02           91.84
## 2944          3420         6       0.02           91.86
## 2945          3425         6       0.02           91.88
## 2946          3440         6       0.02           91.90
## 2947          3441         6       0.02           91.92
## 2948          3445         6       0.02           91.94
## 2949          3457         6       0.02           91.96
## 2950          3461         6       0.02           91.98
## 2951          3473         6       0.02           92.00
## 2952          3485         6       0.02           92.02
## 2953          3530         6       0.02           92.04
## 2954          3532         6       0.02           92.06
## 2955          3534         6       0.02           92.08
## 2956          3538         6       0.02           92.10
## 2957          3553         6       0.02           92.12
## 2958          3569         6       0.02           92.14
## 2959          3578         6       0.02           92.16
## 2960          3597         6       0.02           92.18
## 2961          3628         6       0.02           92.20
## 2962          3641         6       0.02           92.22
## 2963          3650         6       0.02           92.24
## 2964          3676         6       0.02           92.26
## 2965          3678         6       0.02           92.28
## 2966          3722         6       0.02           92.30
## 2967          3724         6       0.02           92.32
## 2968          3726         6       0.02           92.34
## 2969          3750         6       0.02           92.36
## 2970          3753         6       0.02           92.38
## 2971          3754         6       0.02           92.40
## 2972          3755         6       0.02           92.42
## 2973          3798         6       0.02           92.44
## 2974          3799         6       0.02           92.46
## 2975          3800         6       0.02           92.48
## 2976          3805         6       0.02           92.50
## 2977          3807         6       0.02           92.52
## 2978          3810         6       0.02           92.54
## 2979          3820         6       0.02           92.56
## 2980          3836         6       0.02           92.58
## 2981          3838         6       0.02           92.60
## 2982          3853         6       0.02           92.62
## 2983          3870         6       0.02           92.64
## 2984          3876         6       0.02           92.66
## 2985          3914         6       0.02           92.68
## 2986          3916         6       0.02           92.70
## 2987          3945         6       0.02           92.72
## 2988          3955         6       0.02           92.74
## 2989          3958         6       0.02           92.76
## 2990          3974         6       0.02           92.78
## 2991          3977         6       0.02           92.80
## 2992          3984         6       0.02           92.82
## 2993          3989         6       0.02           92.84
## 2994          3996         6       0.02           92.86
## 2995          4010         6       0.02           92.88
## 2996          4016         6       0.02           92.90
## 2997          4021         6       0.02           92.92
## 2998          4033         6       0.02           92.94
## 2999          4034         6       0.02           92.96
## 3000          4051         6       0.02           92.98
## 3001          4053         6       0.02           93.00
## 3002          4061         6       0.02           93.02
## 3003          4064         6       0.02           93.04
## 3004          4067         6       0.02           93.06
## 3005          4070         6       0.02           93.08
## 3006          4079         6       0.02           93.10
## 3007          4081         6       0.02           93.12
## 3008          4089         6       0.02           93.14
## 3009          4090         6       0.02           93.16
## 3010          4095         6       0.02           93.18
## 3011          4136         6       0.02           93.20
## 3012          4139         6       0.02           93.22
## 3013          4140         6       0.02           93.24
## 3014          4145         6       0.02           93.26
## 3015          4157         6       0.02           93.28
## 3016          4159         6       0.02           93.30
## 3017          4167         6       0.02           93.32
## 3018          4185         6       0.02           93.34
## 3019          4189         6       0.02           93.36
## 3020          4225         6       0.02           93.38
## 3021          4241         6       0.02           93.40
## 3022          4254         6       0.02           93.42
## 3023          4256         6       0.02           93.44
## 3024          4270         6       0.02           93.46
## 3025          4287         6       0.02           93.48
## 3026          4318         6       0.02           93.50
## 3027          4331         6       0.02           93.52
## 3028          4339         6       0.02           93.54
## 3029          4345         6       0.02           93.56
## 3030          4358         6       0.02           93.58
## 3031          4360         6       0.02           93.60
## 3032          4363         6       0.02           93.62
## 3033          4381         6       0.02           93.64
## 3034          4400         6       0.02           93.66
## 3035          4407         6       0.02           93.68
## 3036          4411         6       0.02           93.70
## 3037          4420         6       0.02           93.72
## 3038          4422         6       0.02           93.74
## 3039          4428         6       0.02           93.76
## 3040          4458         6       0.02           93.78
## 3041          4484         6       0.02           93.80
## 3042          4488         6       0.02           93.82
## 3043          4507         6       0.02           93.84
## 3044          4520         6       0.02           93.86
## 3045          4532         6       0.02           93.88
## 3046          4533         6       0.02           93.90
## 3047          4542         6       0.02           93.92
## 3048          4543         6       0.02           93.94
## 3049          4558         6       0.02           93.96
## 3050          4570         6       0.02           93.98
## 3051          4571         6       0.02           94.00
## 3052          4577         6       0.02           94.02
## 3053          4581         6       0.02           94.04
## 3054          4597         6       0.02           94.06
## 3055          4605         6       0.02           94.08
## 3056          4644         6       0.02           94.10
## 3057          4663         6       0.02           94.12
## 3058          4668         6       0.02           94.14
## 3059          4674         6       0.02           94.16
## 3060          4682         6       0.02           94.18
## 3061          4706         6       0.02           94.20
## 3062          4709         6       0.02           94.22
## 3063          4713         6       0.02           94.24
## 3064          4723         6       0.02           94.26
## 3065          4729         6       0.02           94.28
## 3066          4731         6       0.02           94.30
## 3067          4738         6       0.02           94.32
## 3068          4751         6       0.02           94.34
## 3069          4781         6       0.02           94.36
## 3070          4803         6       0.02           94.38
## 3071          4848         6       0.02           94.40
## 3072          4858         6       0.02           94.42
## 3073          4861         6       0.02           94.44
## 3074          4866         6       0.02           94.46
## 3075          4870         6       0.02           94.48
## 3076          4880         6       0.02           94.50
## 3077          4887         6       0.02           94.52
## 3078          4888         6       0.02           94.54
## 3079          4898         6       0.02           94.56
## 3080          4902         6       0.02           94.58
## 3081          4909         6       0.02           94.60
## 3082          4910         6       0.02           94.62
## 3083          4917         6       0.02           94.64
## 3084          4943         6       0.02           94.66
## 3085          4955         6       0.02           94.68
## 3086          4957         6       0.02           94.70
## 3087          4966         6       0.02           94.72
## 3088          4971         6       0.02           94.74
## 3089          4983         6       0.02           94.76
## 3090          4997         6       0.02           94.78
## 3091          1059         5       0.01           94.79
## 3092          1080         5       0.01           94.80
## 3093          1082         5       0.01           94.81
## 3094          1151         5       0.01           94.82
## 3095          1164         5       0.01           94.83
## 3096          1179         5       0.01           94.84
## 3097          1184         5       0.01           94.85
## 3098          1192         5       0.01           94.86
## 3099          1236         5       0.01           94.87
## 3100          1249         5       0.01           94.88
## 3101          1254         5       0.01           94.89
## 3102          1318         5       0.01           94.90
## 3103          1321         5       0.01           94.91
## 3104          1334         5       0.01           94.92
## 3105          1338         5       0.01           94.93
## 3106          1362         5       0.01           94.94
## 3107          1367         5       0.01           94.95
## 3108          1429         5       0.01           94.96
## 3109          1464         5       0.01           94.97
## 3110          1467         5       0.01           94.98
## 3111          1506         5       0.01           94.99
## 3112          1525         5       0.01           95.00
## 3113          1530         5       0.01           95.01
## 3114          1537         5       0.01           95.02
## 3115          1539         5       0.01           95.03
## 3116          1563         5       0.01           95.04
## 3117          1570         5       0.01           95.05
## 3118          1631         5       0.01           95.06
## 3119          1644         5       0.01           95.07
## 3120          1645         5       0.01           95.08
## 3121          1662         5       0.01           95.09
## 3122          1683         5       0.01           95.10
## 3123          1689         5       0.01           95.11
## 3124          1712         5       0.01           95.12
## 3125          1714         5       0.01           95.13
## 3126          1735         5       0.01           95.14
## 3127          1766         5       0.01           95.15
## 3128          1769         5       0.01           95.16
## 3129          1794         5       0.01           95.17
## 3130          1840         5       0.01           95.18
## 3131          1857         5       0.01           95.19
## 3132          1858         5       0.01           95.20
## 3133          1861         5       0.01           95.21
## 3134          1875         5       0.01           95.22
## 3135          1907         5       0.01           95.23
## 3136          1941         5       0.01           95.24
## 3137          1972         5       0.01           95.25
## 3138          1974         5       0.01           95.26
## 3139          2027         5       0.01           95.27
## 3140          2046         5       0.01           95.28
## 3141          2057         5       0.01           95.29
## 3142          2060         5       0.01           95.30
## 3143          2080         5       0.01           95.31
## 3144          2088         5       0.01           95.32
## 3145          2105         5       0.01           95.33
## 3146          2118         5       0.01           95.34
## 3147          2145         5       0.01           95.35
## 3148          2172         5       0.01           95.36
## 3149          2180         5       0.01           95.37
## 3150          2192         5       0.01           95.38
## 3151          2227         5       0.01           95.39
## 3152          2246         5       0.01           95.40
## 3153          2313         5       0.01           95.41
## 3154          2334         5       0.01           95.42
## 3155          2335         5       0.01           95.43
## 3156          2377         5       0.01           95.44
## 3157          2395         5       0.01           95.45
## 3158          2461         5       0.01           95.46
## 3159          2462         5       0.01           95.47
## 3160          2478         5       0.01           95.48
## 3161          2486         5       0.01           95.49
## 3162          2493         5       0.01           95.50
## 3163          2527         5       0.01           95.51
## 3164          2546         5       0.01           95.52
## 3165          2583         5       0.01           95.53
## 3166          2586         5       0.01           95.54
## 3167          2588         5       0.01           95.55
## 3168          2609         5       0.01           95.56
## 3169          2634         5       0.01           95.57
## 3170          2638         5       0.01           95.58
## 3171          2655         5       0.01           95.59
## 3172          2667         5       0.01           95.60
## 3173          2728         5       0.01           95.61
## 3174          2767         5       0.01           95.62
## 3175          2770         5       0.01           95.63
## 3176          2797         5       0.01           95.64
## 3177          2823         5       0.01           95.65
## 3178          2853         5       0.01           95.66
## 3179          2891         5       0.01           95.67
## 3180          2892         5       0.01           95.68
## 3181          2923         5       0.01           95.69
## 3182          2936         5       0.01           95.70
## 3183          2945         5       0.01           95.71
## 3184          2949         5       0.01           95.72
## 3185          2976         5       0.01           95.73
## 3186          2995         5       0.01           95.74
## 3187          2998         5       0.01           95.75
## 3188          3008         5       0.01           95.76
## 3189          3019         5       0.01           95.77
## 3190          3024         5       0.01           95.78
## 3191          3037         5       0.01           95.79
## 3192          3047         5       0.01           95.80
## 3193          3052         5       0.01           95.81
## 3194          3057         5       0.01           95.82
## 3195          3073         5       0.01           95.83
## 3196          3074         5       0.01           95.84
## 3197          3078         5       0.01           95.85
## 3198          3147         5       0.01           95.86
## 3199          3191         5       0.01           95.87
## 3200          3196         5       0.01           95.88
## 3201          3198         5       0.01           95.89
## 3202          3218         5       0.01           95.90
## 3203          3231         5       0.01           95.91
## 3204          3250         5       0.01           95.92
## 3205          3269         5       0.01           95.93
## 3206          3319         5       0.01           95.94
## 3207          3330         5       0.01           95.95
## 3208          3332         5       0.01           95.96
## 3209          3341         5       0.01           95.97
## 3210          3359         5       0.01           95.98
## 3211          3374         5       0.01           95.99
## 3212          3379         5       0.01           96.00
## 3213          3434         5       0.01           96.01
## 3214          3567         5       0.01           96.02
## 3215          3602         5       0.01           96.03
## 3216          3634         5       0.01           96.04
## 3217          3647         5       0.01           96.05
## 3218          3654         5       0.01           96.06
## 3219          3655         5       0.01           96.07
## 3220          3696         5       0.01           96.08
## 3221          3734         5       0.01           96.09
## 3222          3747         5       0.01           96.10
## 3223          3813         5       0.01           96.11
## 3224          3834         5       0.01           96.12
## 3225          3837         5       0.01           96.13
## 3226          3868         5       0.01           96.14
## 3227          3884         5       0.01           96.15
## 3228          3885         5       0.01           96.16
## 3229          3889         5       0.01           96.17
## 3230          3892         5       0.01           96.18
## 3231          3939         5       0.01           96.19
## 3232          3964         5       0.01           96.20
## 3233          3968         5       0.01           96.21
## 3234          3969         5       0.01           96.22
## 3235          3978         5       0.01           96.23
## 3236          4020         5       0.01           96.24
## 3237          4052         5       0.01           96.25
## 3238          4054         5       0.01           96.26
## 3239          4087         5       0.01           96.27
## 3240          4099         5       0.01           96.28
## 3241          4161         5       0.01           96.29
## 3242          4198         5       0.01           96.30
## 3243          4231         5       0.01           96.31
## 3244          4271         5       0.01           96.32
## 3245          4311         5       0.01           96.33
## 3246          4327         5       0.01           96.34
## 3247          4385         5       0.01           96.35
## 3248          4390         5       0.01           96.36
## 3249          4393         5       0.01           96.37
## 3250          4402         5       0.01           96.38
## 3251          4475         5       0.01           96.39
## 3252          4480         5       0.01           96.40
## 3253          4513         5       0.01           96.41
## 3254          4518         5       0.01           96.42
## 3255          4519         5       0.01           96.43
## 3256          4611         5       0.01           96.44
## 3257          4615         5       0.01           96.45
## 3258          4619         5       0.01           96.46
## 3259          4625         5       0.01           96.47
## 3260          4784         5       0.01           96.48
## 3261          4801         5       0.01           96.49
## 3262          4829         5       0.01           96.50
## 3263          4846         5       0.01           96.51
## 3264          4865         5       0.01           96.52
## 3265          4874         5       0.01           96.53
## 3266          4907         5       0.01           96.54
## 3267          4918         5       0.01           96.55
## 3268          4927         5       0.01           96.56
## 3269          1005         4       0.01           96.57
## 3270          1024         4       0.01           96.58
## 3271          1044         4       0.01           96.59
## 3272          1046         4       0.01           96.60
## 3273          1063         4       0.01           96.61
## 3274          1068         4       0.01           96.62
## 3275          1070         4       0.01           96.63
## 3276          1072         4       0.01           96.64
## 3277          1112         4       0.01           96.65
## 3278          1124         4       0.01           96.66
## 3279          1166         4       0.01           96.67
## 3280          1167         4       0.01           96.68
## 3281          1177         4       0.01           96.69
## 3282          1180         4       0.01           96.70
## 3283          1189         4       0.01           96.71
## 3284          1193         4       0.01           96.72
## 3285          1201         4       0.01           96.73
## 3286          1219         4       0.01           96.74
## 3287          1222         4       0.01           96.75
## 3288          1224         4       0.01           96.76
## 3289          1247         4       0.01           96.77
## 3290          1257         4       0.01           96.78
## 3291          1260         4       0.01           96.79
## 3292          1263         4       0.01           96.80
## 3293          1273         4       0.01           96.81
## 3294          1284         4       0.01           96.82
## 3295          1292         4       0.01           96.83
## 3296          1310         4       0.01           96.84
## 3297          1337         4       0.01           96.85
## 3298          1359         4       0.01           96.86
## 3299          1378         4       0.01           96.87
## 3300          1394         4       0.01           96.88
## 3301          1401         4       0.01           96.89
## 3302          1402         4       0.01           96.90
## 3303          1411         4       0.01           96.91
## 3304          1415         4       0.01           96.92
## 3305          1433         4       0.01           96.93
## 3306          1437         4       0.01           96.94
## 3307          1448         4       0.01           96.95
## 3308          1453         4       0.01           96.96
## 3309          1459         4       0.01           96.97
## 3310          1462         4       0.01           96.98
## 3311          1471         4       0.01           96.99
## 3312          1481         4       0.01           97.00
## 3313          1485         4       0.01           97.01
## 3314          1490         4       0.01           97.02
## 3315          1511         4       0.01           97.03
## 3316          1516         4       0.01           97.04
## 3317          1531         4       0.01           97.05
## 3318          1557         4       0.01           97.06
## 3319          1568         4       0.01           97.07
## 3320          1589         4       0.01           97.08
## 3321          1614         4       0.01           97.09
## 3322          1630         4       0.01           97.10
## 3323          1640         4       0.01           97.11
## 3324          1643         4       0.01           97.12
## 3325          1666         4       0.01           97.13
## 3326          1700         4       0.01           97.14
## 3327          1707         4       0.01           97.15
## 3328          1709         4       0.01           97.16
## 3329          1739         4       0.01           97.17
## 3330          1744         4       0.01           97.18
## 3331          1755         4       0.01           97.19
## 3332          1762         4       0.01           97.20
## 3333          1790         4       0.01           97.21
## 3334          1795         4       0.01           97.22
## 3335          1812         4       0.01           97.23
## 3336          1830         4       0.01           97.24
## 3337          1841         4       0.01           97.25
## 3338          1860         4       0.01           97.26
## 3339          1880         4       0.01           97.27
## 3340          1886         4       0.01           97.28
## 3341          1915         4       0.01           97.29
## 3342          1918         4       0.01           97.30
## 3343          1919         4       0.01           97.31
## 3344          1942         4       0.01           97.32
## 3345          1944         4       0.01           97.33
## 3346          1953         4       0.01           97.34
## 3347          1957         4       0.01           97.35
## 3348          1960         4       0.01           97.36
## 3349          1965         4       0.01           97.37
## 3350          1975         4       0.01           97.38
## 3351          1981         4       0.01           97.39
## 3352          2006         4       0.01           97.40
## 3353          2012         4       0.01           97.41
## 3354          2015         4       0.01           97.42
## 3355          2016         4       0.01           97.43
## 3356          2024         4       0.01           97.44
## 3357          2026         4       0.01           97.45
## 3358          2039         4       0.01           97.46
## 3359          2050         4       0.01           97.47
## 3360          2084         4       0.01           97.48
## 3361          2112         4       0.01           97.49
## 3362          2116         4       0.01           97.50
## 3363          2121         4       0.01           97.51
## 3364          2137         4       0.01           97.52
## 3365          2153         4       0.01           97.53
## 3366          2161         4       0.01           97.54
## 3367          2173         4       0.01           97.55
## 3368          2179         4       0.01           97.56
## 3369          2199         4       0.01           97.57
## 3370          2214         4       0.01           97.58
## 3371          2228         4       0.01           97.59
## 3372          2249         4       0.01           97.60
## 3373          2275         4       0.01           97.61
## 3374          2280         4       0.01           97.62
## 3375          2285         4       0.01           97.63
## 3376          2322         4       0.01           97.64
## 3377          2329         4       0.01           97.65
## 3378          2330         4       0.01           97.66
## 3379          2342         4       0.01           97.67
## 3380          2347         4       0.01           97.68
## 3381          2350         4       0.01           97.69
## 3382          2378         4       0.01           97.70
## 3383          2423         4       0.01           97.71
## 3384          2425         4       0.01           97.72
## 3385          2429         4       0.01           97.73
## 3386          2438         4       0.01           97.74
## 3387          2455         4       0.01           97.75
## 3388          2487         4       0.01           97.76
## 3389          2501         4       0.01           97.77
## 3390          2526         4       0.01           97.78
## 3391          2531         4       0.01           97.79
## 3392          2539         4       0.01           97.80
## 3393          2575         4       0.01           97.81
## 3394          2576         4       0.01           97.82
## 3395          2591         4       0.01           97.83
## 3396          2603         4       0.01           97.84
## 3397          2607         4       0.01           97.85
## 3398          2615         4       0.01           97.86
## 3399          2621         4       0.01           97.87
## 3400          2624         4       0.01           97.88
## 3401          2637         4       0.01           97.89
## 3402          2651         4       0.01           97.90
## 3403          2660         4       0.01           97.91
## 3404          2665         4       0.01           97.92
## 3405          2686         4       0.01           97.93
## 3406          2697         4       0.01           97.94
## 3407          2710         4       0.01           97.95
## 3408          2722         4       0.01           97.96
## 3409          2725         4       0.01           97.97
## 3410          2731         4       0.01           97.98
## 3411          2739         4       0.01           97.99
## 3412          2740         4       0.01           98.00
## 3413          2776         4       0.01           98.01
## 3414          2812         4       0.01           98.02
## 3415          2822         4       0.01           98.03
## 3416          2833         4       0.01           98.04
## 3417          2842         4       0.01           98.05
## 3418          2845         4       0.01           98.06
## 3419          2848         4       0.01           98.07
## 3420          2856         4       0.01           98.08
## 3421          2859         4       0.01           98.09
## 3422          2878         4       0.01           98.10
## 3423          2881         4       0.01           98.11
## 3424          2886         4       0.01           98.12
## 3425          2887         4       0.01           98.13
## 3426          2911         4       0.01           98.14
## 3427          2913         4       0.01           98.15
## 3428          2915         4       0.01           98.16
## 3429          2919         4       0.01           98.17
## 3430          2929         4       0.01           98.18
## 3431          2963         4       0.01           98.19
## 3432          2983         4       0.01           98.20
## 3433          3001         4       0.01           98.21
## 3434          3004         4       0.01           98.22
## 3435          3007         4       0.01           98.23
## 3436          3032         4       0.01           98.24
## 3437          3040         4       0.01           98.25
## 3438          3049         4       0.01           98.26
## 3439          3056         4       0.01           98.27
## 3440          3064         4       0.01           98.28
## 3441          3076         4       0.01           98.29
## 3442          3085         4       0.01           98.30
## 3443          3098         4       0.01           98.31
## 3444          3103         4       0.01           98.32
## 3445          3108         4       0.01           98.33
## 3446          3125         4       0.01           98.34
## 3447          3131         4       0.01           98.35
## 3448          3146         4       0.01           98.36
## 3449          3152         4       0.01           98.37
## 3450          3163         4       0.01           98.38
## 3451          3174         4       0.01           98.39
## 3452          3177         4       0.01           98.40
## 3453          3211         4       0.01           98.41
## 3454          3212         4       0.01           98.42
## 3455          3216         4       0.01           98.43
## 3456          3240         4       0.01           98.44
## 3457          3249         4       0.01           98.45
## 3458          3253         4       0.01           98.46
## 3459          3272         4       0.01           98.47
## 3460          3278         4       0.01           98.48
## 3461          3286         4       0.01           98.49
## 3462          3291         4       0.01           98.50
## 3463          3318         4       0.01           98.51
## 3464          3326         4       0.01           98.52
## 3465          3333         4       0.01           98.53
## 3466          3335         4       0.01           98.54
## 3467          3350         4       0.01           98.55
## 3468          3366         4       0.01           98.56
## 3469          3373         4       0.01           98.57
## 3470          3381         4       0.01           98.58
## 3471          3395         4       0.01           98.59
## 3472          3404         4       0.01           98.60
## 3473          3412         4       0.01           98.61
## 3474          3418         4       0.01           98.62
## 3475          3432         4       0.01           98.63
## 3476          3453         4       0.01           98.64
## 3477          3464         4       0.01           98.65
## 3478          3501         4       0.01           98.66
## 3479          3512         4       0.01           98.67
## 3480          3514         4       0.01           98.68
## 3481          3541         4       0.01           98.69
## 3482          3542         4       0.01           98.70
## 3483          3566         4       0.01           98.71
## 3484          3572         4       0.01           98.72
## 3485          3580         4       0.01           98.73
## 3486          3585         4       0.01           98.74
## 3487          3594         4       0.01           98.75
## 3488          3598         4       0.01           98.76
## 3489          3610         4       0.01           98.77
## 3490          3618         4       0.01           98.78
## 3491          3623         4       0.01           98.79
## 3492          3626         4       0.01           98.80
## 3493          3627         4       0.01           98.81
## 3494          3630         4       0.01           98.82
## 3495          3632         4       0.01           98.83
## 3496          3638         4       0.01           98.84
## 3497          3652         4       0.01           98.85
## 3498          3707         4       0.01           98.86
## 3499          3711         4       0.01           98.87
## 3500          3714         4       0.01           98.88
## 3501          3725         4       0.01           98.89
## 3502          3733         4       0.01           98.90
## 3503          3742         4       0.01           98.91
## 3504          3791         4       0.01           98.92
## 3505          3792         4       0.01           98.93
## 3506          3802         4       0.01           98.94
## 3507          3859         4       0.01           98.95
## 3508          3883         4       0.01           98.96
## 3509          3888         4       0.01           98.97
## 3510          3901         4       0.01           98.98
## 3511          3906         4       0.01           98.99
## 3512          3908         4       0.01           99.00
## 3513          3933         4       0.01           99.01
## 3514          3936         4       0.01           99.02
## 3515          3940         4       0.01           99.03
## 3516          3975         4       0.01           99.04
## 3517          3979         4       0.01           99.05
## 3518          3981         4       0.01           99.06
## 3519          3992         4       0.01           99.07
## 3520          3995         4       0.01           99.08
## 3521          4005         4       0.01           99.09
## 3522          4027         4       0.01           99.10
## 3523          4032         4       0.01           99.11
## 3524          4047         4       0.01           99.12
## 3525          4093         4       0.01           99.13
## 3526          4123         4       0.01           99.14
## 3527          4135         4       0.01           99.15
## 3528          4143         4       0.01           99.16
## 3529          4158         4       0.01           99.17
## 3530          4168         4       0.01           99.18
## 3531          4173         4       0.01           99.19
## 3532          4174         4       0.01           99.20
## 3533          4205         4       0.01           99.21
## 3534          4209         4       0.01           99.22
## 3535          4210         4       0.01           99.23
## 3536          4239         4       0.01           99.24
## 3537          4250         4       0.01           99.25
## 3538          4278         4       0.01           99.26
## 3539          4282         4       0.01           99.27
## 3540          4309         4       0.01           99.28
## 3541          4317         4       0.01           99.29
## 3542          4332         4       0.01           99.30
## 3543          4347         4       0.01           99.31
## 3544          4354         4       0.01           99.32
## 3545          4365         4       0.01           99.33
## 3546          4374         4       0.01           99.34
## 3547          4378         4       0.01           99.35
## 3548          4379         4       0.01           99.36
## 3549          4382         4       0.01           99.37
## 3550          4383         4       0.01           99.38
## 3551          4396         4       0.01           99.39
## 3552          4452         4       0.01           99.40
## 3553          4465         4       0.01           99.41
## 3554          4481         4       0.01           99.42
## 3555          4483         4       0.01           99.43
## 3556          4490         4       0.01           99.44
## 3557          4497         4       0.01           99.45
## 3558          4528         4       0.01           99.46
## 3559          4530         4       0.01           99.47
## 3560          4534         4       0.01           99.48
## 3561          4551         4       0.01           99.49
## 3562          4560         4       0.01           99.50
## 3563          4562         4       0.01           99.51
## 3564          4595         4       0.01           99.52
## 3565          4599         4       0.01           99.53
## 3566          4604         4       0.01           99.54
## 3567          4609         4       0.01           99.55
## 3568          4612         4       0.01           99.56
## 3569          4627         4       0.01           99.57
## 3570          4642         4       0.01           99.58
## 3571          4647         4       0.01           99.59
## 3572          4653         4       0.01           99.60
## 3573          4707         4       0.01           99.61
## 3574          4714         4       0.01           99.62
## 3575          4716         4       0.01           99.63
## 3576          4724         4       0.01           99.64
## 3577          4730         4       0.01           99.65
## 3578          4739         4       0.01           99.66
## 3579          4768         4       0.01           99.67
## 3580          4774         4       0.01           99.68
## 3581          4791         4       0.01           99.69
## 3582          4792         4       0.01           99.70
## 3583          4805         4       0.01           99.71
## 3584          4810         4       0.01           99.72
## 3585          4850         4       0.01           99.73
## 3586          4857         4       0.01           99.74
## 3587          4863         4       0.01           99.75
## 3588          4882         4       0.01           99.76
## 3589          4900         4       0.01           99.77
## 3590          4920         4       0.01           99.78
## 3591          4936         4       0.01           99.79
## 3592          4948         4       0.01           99.80
## 3593          4964         4       0.01           99.81
## 3594          4965         4       0.01           99.82
## 3595          4974         4       0.01           99.83
## 3596          4995         4       0.01           99.84
## 3597          1071         3       0.01           99.85
## 3598          1117         3       0.01           99.86
## 3599          1228         3       0.01           99.87
## 3600          1251         3       0.01           99.88
## 3601          1439         3       0.01           99.89
## 3602          1447         3       0.01           99.90
## 3603          1813         3       0.01           99.91
## 3604          1976         3       0.01           99.92
## 3605          1977         3       0.01           99.93
## 3606          2123         3       0.01           99.94
## 3607          2282         3       0.01           99.95
## 3608          2482         3       0.01           99.96
## 3609          2566         3       0.01           99.97
## 3610          2598         3       0.01           99.98
## 3611          2684         3       0.01           99.99
## 3612          2734         3       0.01          100.00
## 3613          2858         3       0.01          100.01
## 3614          2895         3       0.01          100.02
## 3615          2931         3       0.01          100.03
## 3616          2953         3       0.01          100.04
## 3617          2992         3       0.01          100.05
## 3618          3124         3       0.01          100.06
## 3619          3149         3       0.01          100.07
## 3620          3171         3       0.01          100.08
## 3621          3197         3       0.01          100.09
## 3622          3223         3       0.01          100.10
## 3623          3376         3       0.01          100.11
## 3624          3477         3       0.01          100.12
## 3625          3536         3       0.01          100.13
## 3626          3555         3       0.01          100.14
## 3627          3565         3       0.01          100.15
## 3628          3605         3       0.01          100.16
## 3629          3648         3       0.01          100.17
## 3630          3700         3       0.01          100.18
## 3631          3770         3       0.01          100.19
## 3632          3887         3       0.01          100.20
## 3633          3941         3       0.01          100.21
## 3634          3944         3       0.01          100.22
## 3635          3993         3       0.01          100.23
## 3636          4055         3       0.01          100.24
## 3637          4141         3       0.01          100.25
## 3638          4181         3       0.01          100.26
## 3639          4186         3       0.01          100.27
## 3640          4200         3       0.01          100.28
## 3641          4429         3       0.01          100.29
## 3642          4454         3       0.01          100.30
## 3643          4602         3       0.01          100.31
## 3644          4755         3       0.01          100.32
## 3645          4775         3       0.01          100.33
## 3646          4889         3       0.01          100.34
## 3647          4928         3       0.01          100.35
## 3648          4930         3       0.01          100.36
## 3649          4973         3       0.01          100.37
## 3650          4982         3       0.01          100.38
## 3651          1019         2       0.01          100.39
## 3652          1029         2       0.01          100.40
## 3653          1036         2       0.01          100.41
## 3654          1039         2       0.01          100.42
## 3655          1084         2       0.01          100.43
## 3656          1089         2       0.01          100.44
## 3657          1093         2       0.01          100.45
## 3658          1096         2       0.01          100.46
## 3659          1119         2       0.01          100.47
## 3660          1121         2       0.01          100.48
## 3661          1156         2       0.01          100.49
## 3662          1221         2       0.01          100.50
## 3663          1227         2       0.01          100.51
## 3664          1238         2       0.01          100.52
## 3665          1243         2       0.01          100.53
## 3666          1250         2       0.01          100.54
## 3667          1255         2       0.01          100.55
## 3668          1266         2       0.01          100.56
## 3669          1267         2       0.01          100.57
## 3670          1272         2       0.01          100.58
## 3671          1300         2       0.01          100.59
## 3672          1313         2       0.01          100.60
## 3673          1314         2       0.01          100.61
## 3674          1352         2       0.01          100.62
## 3675          1368         2       0.01          100.63
## 3676          1375         2       0.01          100.64
## 3677          1397         2       0.01          100.65
## 3678          1400         2       0.01          100.66
## 3679          1414         2       0.01          100.67
## 3680          1436         2       0.01          100.68
## 3681          1455         2       0.01          100.69
## 3682          1469         2       0.01          100.70
## 3683          1470         2       0.01          100.71
## 3684          1496         2       0.01          100.72
## 3685          1519         2       0.01          100.73
## 3686          1552         2       0.01          100.74
## 3687          1555         2       0.01          100.75
## 3688          1556         2       0.01          100.76
## 3689          1558         2       0.01          100.77
## 3690          1560         2       0.01          100.78
## 3691          1577         2       0.01          100.79
## 3692          1579         2       0.01          100.80
## 3693          1592         2       0.01          100.81
## 3694          1626         2       0.01          100.82
## 3695          1642         2       0.01          100.83
## 3696          1667         2       0.01          100.84
## 3697          1673         2       0.01          100.85
## 3698          1688         2       0.01          100.86
## 3699          1695         2       0.01          100.87
## 3700          1701         2       0.01          100.88
## 3701          1745         2       0.01          100.89
## 3702          1775         2       0.01          100.90
## 3703          1826         2       0.01          100.91
## 3704          1871         2       0.01          100.92
## 3705          1876         2       0.01          100.93
## 3706          1898         2       0.01          100.94
## 3707          1925         2       0.01          100.95
## 3708          1933         2       0.01          100.96
## 3709          1956         2       0.01          100.97
## 3710          1963         2       0.01          100.98
## 3711          1973         2       0.01          100.99
## 3712          1989         2       0.01          101.00
## 3713          2021         2       0.01          101.01
## 3714          2096         2       0.01          101.02
## 3715          2103         2       0.01          101.03
## 3716          2126         2       0.01          101.04
## 3717          2136         2       0.01          101.05
## 3718          2197         2       0.01          101.06
## 3719          2198         2       0.01          101.07
## 3720          2203         2       0.01          101.08
## 3721          2213         2       0.01          101.09
## 3722          2216         2       0.01          101.10
## 3723          2248         2       0.01          101.11
## 3724          2263         2       0.01          101.12
## 3725          2281         2       0.01          101.13
## 3726          2292         2       0.01          101.14
## 3727          2296         2       0.01          101.15
## 3728          2297         2       0.01          101.16
## 3729          2302         2       0.01          101.17
## 3730          2304         2       0.01          101.18
## 3731          2373         2       0.01          101.19
## 3732          2387         2       0.01          101.20
## 3733          2414         2       0.01          101.21
## 3734          2417         2       0.01          101.22
## 3735          2442         2       0.01          101.23
## 3736          2456         2       0.01          101.24
## 3737          2474         2       0.01          101.25
## 3738          2497         2       0.01          101.26
## 3739          2503         2       0.01          101.27
## 3740          2558         2       0.01          101.28
## 3741          2567         2       0.01          101.29
## 3742          2572         2       0.01          101.30
## 3743          2614         2       0.01          101.31
## 3744          2628         2       0.01          101.32
## 3745          2640         2       0.01          101.33
## 3746          2668         2       0.01          101.34
## 3747          2714         2       0.01          101.35
## 3748          2717         2       0.01          101.36
## 3749          2720         2       0.01          101.37
## 3750          2735         2       0.01          101.38
## 3751          2748         2       0.01          101.39
## 3752          2752         2       0.01          101.40
## 3753          2759         2       0.01          101.41
## 3754          2773         2       0.01          101.42
## 3755          2783         2       0.01          101.43
## 3756          2791         2       0.01          101.44
## 3757          2820         2       0.01          101.45
## 3758          2826         2       0.01          101.46
## 3759          2828         2       0.01          101.47
## 3760          2841         2       0.01          101.48
## 3761          2844         2       0.01          101.49
## 3762          2852         2       0.01          101.50
## 3763          2866         2       0.01          101.51
## 3764          2889         2       0.01          101.52
## 3765          2894         2       0.01          101.53
## 3766          2968         2       0.01          101.54
## 3767          2987         2       0.01          101.55
## 3768          2988         2       0.01          101.56
## 3769          3000         2       0.01          101.57
## 3770          3043         2       0.01          101.58
## 3771          3080         2       0.01          101.59
## 3772          3093         2       0.01          101.60
## 3773          3097         2       0.01          101.61
## 3774          3105         2       0.01          101.62
## 3775          3126         2       0.01          101.63
## 3776          3134         2       0.01          101.64
## 3777          3136         2       0.01          101.65
## 3778          3155         2       0.01          101.66
## 3779          3162         2       0.01          101.67
## 3780          3173         2       0.01          101.68
## 3781          3179         2       0.01          101.69
## 3782          3199         2       0.01          101.70
## 3783          3230         2       0.01          101.71
## 3784          3233         2       0.01          101.72
## 3785          3234         2       0.01          101.73
## 3786          3239         2       0.01          101.74
## 3787          3243         2       0.01          101.75
## 3788          3270         2       0.01          101.76
## 3789          3290         2       0.01          101.77
## 3790          3301         2       0.01          101.78
## 3791          3314         2       0.01          101.79
## 3792          3336         2       0.01          101.80
## 3793          3345         2       0.01          101.81
## 3794          3362         2       0.01          101.82
## 3795          3367         2       0.01          101.83
## 3796          3372         2       0.01          101.84
## 3797          3377         2       0.01          101.85
## 3798          3391         2       0.01          101.86
## 3799          3422         2       0.01          101.87
## 3800          3431         2       0.01          101.88
## 3801          3436         2       0.01          101.89
## 3802          3448         2       0.01          101.90
## 3803          3454         2       0.01          101.91
## 3804          3478         2       0.01          101.92
## 3805          3490         2       0.01          101.93
## 3806          3503         2       0.01          101.94
## 3807          3510         2       0.01          101.95
## 3808          3533         2       0.01          101.96
## 3809          3576         2       0.01          101.97
## 3810          3606         2       0.01          101.98
## 3811          3607         2       0.01          101.99
## 3812          3624         2       0.01          102.00
## 3813          3625         2       0.01          102.01
## 3814          3631         2       0.01          102.02
## 3815          3706         2       0.01          102.03
## 3816          3723         2       0.01          102.04
## 3817          3740         2       0.01          102.05
## 3818          3771         2       0.01          102.06
## 3819          3777         2       0.01          102.07
## 3820          3780         2       0.01          102.08
## 3821          3788         2       0.01          102.09
## 3822          3796         2       0.01          102.10
## 3823          3823         2       0.01          102.11
## 3824          3824         2       0.01          102.12
## 3825          3825         2       0.01          102.13
## 3826          3826         2       0.01          102.14
## 3827          3845         2       0.01          102.15
## 3828          3858         2       0.01          102.16
## 3829          3874         2       0.01          102.17
## 3830          3932         2       0.01          102.18
## 3831          3943         2       0.01          102.19
## 3832          3949         2       0.01          102.20
## 3833          3970         2       0.01          102.21
## 3834          3990         2       0.01          102.22
## 3835          3991         2       0.01          102.23
## 3836          3994         2       0.01          102.24
## 3837          4011         2       0.01          102.25
## 3838          4023         2       0.01          102.26
## 3839          4029         2       0.01          102.27
## 3840          4043         2       0.01          102.28
## 3841          4062         2       0.01          102.29
## 3842          4072         2       0.01          102.30
## 3843          4083         2       0.01          102.31
## 3844          4118         2       0.01          102.32
## 3845          4142         2       0.01          102.33
## 3846          4151         2       0.01          102.34
## 3847          4188         2       0.01          102.35
## 3848          4208         2       0.01          102.36
## 3849          4237         2       0.01          102.37
## 3850          4247         2       0.01          102.38
## 3851          4248         2       0.01          102.39
## 3852          4279         2       0.01          102.40
## 3853          4307         2       0.01          102.41
## 3854          4333         2       0.01          102.42
## 3855          4366         2       0.01          102.43
## 3856          4386         2       0.01          102.44
## 3857          4419         2       0.01          102.45
## 3858          4423         2       0.01          102.46
## 3859          4425         2       0.01          102.47
## 3860          4436         2       0.01          102.48
## 3861          4447         2       0.01          102.49
## 3862          4451         2       0.01          102.50
## 3863          4472         2       0.01          102.51
## 3864          4491         2       0.01          102.52
## 3865          4496         2       0.01          102.53
## 3866          4506         2       0.01          102.54
## 3867          4514         2       0.01          102.55
## 3868          4517         2       0.01          102.56
## 3869          4521         2       0.01          102.57
## 3870          4565         2       0.01          102.58
## 3871          4587         2       0.01          102.59
## 3872          4590         2       0.01          102.60
## 3873          4621         2       0.01          102.61
## 3874          4630         2       0.01          102.62
## 3875          4631         2       0.01          102.63
## 3876          4639         2       0.01          102.64
## 3877          4703         2       0.01          102.65
## 3878          4732         2       0.01          102.66
## 3879          4737         2       0.01          102.67
## 3880          4795         2       0.01          102.68
## 3881          4802         2       0.01          102.69
## 3882          4815         2       0.01          102.70
## 3883          4816         2       0.01          102.71
## 3884          4824         2       0.01          102.72
## 3885          4834         2       0.01          102.73
## 3886          4844         2       0.01          102.74
## 3887          4884         2       0.01          102.75
## 3888          4885         2       0.01          102.76
## 3889          4904         2       0.01          102.77
## 3890          4905         2       0.01          102.78
## 3891          4926         2       0.01          102.79
## 3892          4945         2       0.01          102.80
## 3893          4949         2       0.01          102.81
## 3894          4961         2       0.01          102.82
## 3895          4978         2       0.01          102.83
## 3896          4980         2       0.01          102.84
## 3897          4994         2       0.01          102.85
## 3898          4998         2       0.01          100.00
## Warning in freq_logic(data = data, input = input[i], plot, na.rm, path_out
## = path_out): Skipping plot for variable 'itemDescription' (more than 100
## categories)
##               itemDescription frequency percentage cumulative_perc
## 1                  whole milk      2502       6.45            6.45
## 2            other vegetables      1898       4.90           11.35
## 3                  rolls/buns      1716       4.43           15.78
## 4                        soda      1514       3.91           19.69
## 5                      yogurt      1334       3.44           23.13
## 6             root vegetables      1071       2.76           25.89
## 7              tropical fruit      1032       2.66           28.55
## 8               bottled water       933       2.41           30.96
## 9                     sausage       924       2.38           33.34
## 10               citrus fruit       812       2.09           35.43
## 11                     pastry       785       2.03           37.46
## 12                  pip fruit       744       1.92           39.38
## 13              shopping bags       731       1.89           41.27
## 14                canned beer       717       1.85           43.12
## 15               bottled beer       687       1.77           44.89
## 16         whipped/sour cream       662       1.71           46.60
## 17                 newspapers       596       1.54           48.14
## 18                frankfurter       580       1.50           49.64
## 19                brown bread       571       1.47           51.11
## 20              domestic eggs       566       1.46           52.57
## 21                       pork       566       1.46           54.03
## 22                     butter       534       1.38           55.41
## 23      fruit/vegetable juice       518       1.34           56.75
## 24                       beef       516       1.33           58.08
## 25                       curd       514       1.33           59.41
## 26                  margarine       491       1.27           60.68
## 27                     coffee       476       1.23           61.91
## 28          frozen vegetables       425       1.10           63.01
## 29                    chicken       422       1.09           64.10
## 30                white bread       362       0.93           65.03
## 31              cream cheese        358       0.92           65.95
## 32                  chocolate       357       0.92           66.87
## 33                    dessert       356       0.92           67.79
## 34                    napkins       335       0.86           68.65
## 35                    berries       327       0.84           69.49
## 36             hamburger meat       327       0.84           70.33
## 37                   UHT-milk       323       0.83           71.16
## 38                     onions       305       0.79           71.95
## 39                salty snack       283       0.73           72.68
## 40                    waffles       280       0.72           73.40
## 41   long life bakery product       269       0.69           74.09
## 42                      sugar       265       0.68           74.77
## 43                butter milk       263       0.68           75.45
## 44                        ham       256       0.66           76.11
## 45                       meat       254       0.66           76.77
## 46               frozen meals       252       0.65           77.42
## 47                  beverages       251       0.65           78.07
## 48        specialty chocolate       240       0.62           78.69
## 49            misc. beverages       238       0.61           79.30
## 50                  ice cream       227       0.59           79.89
## 51                        oil       225       0.58           80.47
## 52                     grapes       220       0.57           81.04
## 53                hard cheese       220       0.57           81.61
## 54                      candy       219       0.56           82.17
## 55              sliced cheese       212       0.55           82.72
## 56              specialty bar       210       0.54           83.26
## 57           hygiene articles       208       0.54           83.80
## 58                chewing gum       181       0.47           84.27
## 59                   cat food       177       0.46           84.73
## 60                 white wine       176       0.45           85.18
## 61                      herbs       159       0.41           85.59
## 62             red/blush wine       157       0.41           86.00
## 63           processed cheese       152       0.39           86.39
## 64                soft cheese       152       0.39           86.78
## 65                      flour       146       0.38           87.16
## 66        semi-finished bread       142       0.37           87.53
## 67                     dishes       135       0.35           87.88
## 68         pickled vegetables       134       0.35           88.23
## 69                  detergent       130       0.34           88.57
## 70  packaged fruit/vegetables       128       0.33           88.90
## 71              baking powder       122       0.31           89.21
## 72                      pasta       121       0.31           89.52
## 73                 pot plants       118       0.30           89.82
## 74                canned fish       116       0.30           90.12
## 75          seasonal products       106       0.27           90.39
## 76                     liquor       103       0.27           90.66
## 77                frozen fish       102       0.26           90.92
## 78              spread cheese       100       0.26           91.18
## 79             condensed milk        98       0.25           91.43
## 80                   cake bar        93       0.24           91.67
## 81             frozen dessert        92       0.24           91.91
## 82                    mustard        92       0.24           92.15
## 83                       salt        89       0.23           92.38
## 84                   pet care        85       0.22           92.60
## 85          canned vegetables        82       0.21           92.81
## 86             roll products         82       0.21           93.02
## 87                     turkey        80       0.21           93.23
## 88                 photo/film        79       0.20           93.43
## 89                 mayonnaise        75       0.19           93.62
## 90            cling film/bags        74       0.19           93.81
## 91               dish cleaner        73       0.19           94.00
## 92     frozen potato products        72       0.19           94.19
## 93           specialty cheese        72       0.19           94.38
## 94             flower (seeds)        70       0.18           94.56
## 95              sweet spreads        69       0.18           94.74
## 96                   dog food        67       0.17           94.91
## 97         liquor (appetizer)        67       0.17           95.08
## 98                    candles        66       0.17           95.25
## 99          finished products        64       0.17           95.42
## 100            instant coffee        61       0.16           95.58
## 101     chocolate marshmallow        60       0.15           95.73
## 102     Instant food products        60       0.15           95.88
## 103                  zwieback        60       0.15           96.03
## 104                   vinegar        51       0.13           96.16
## 105                liver loaf        50       0.13           96.29
## 106                      rice        49       0.13           96.42
## 107                   popcorn        48       0.12           96.54
## 108                     soups        48       0.12           96.66
## 109               curd cheese        46       0.12           96.78
## 110            sparkling wine        46       0.12           96.90
## 111    house keeping products        45       0.12           97.02
## 112                    sauces        44       0.11           97.13
## 113                   cereals        42       0.11           97.24
## 114                  softener        41       0.11           97.35
## 115  female sanitary products        40       0.10           97.45
## 116                    spices        40       0.10           97.55
## 117                    brandy        38       0.10           97.65
## 118            male cosmetics        37       0.10           97.75
## 119              meat spreads        35       0.09           97.84
## 120                       jam        34       0.09           97.93
## 121               dental care        33       0.09           98.02
## 122               nuts/prunes        33       0.09           98.11
## 123                   ketchup        32       0.08           98.19
## 124                       rum        32       0.08           98.27
## 125                   cleaner        31       0.08           98.35
## 126            kitchen towels        30       0.08           98.43
## 127          artif. sweetener        29       0.07           98.50
## 128                      fish        29       0.07           98.57
## 129               light bulbs        29       0.07           98.64
## 130             specialty fat        29       0.07           98.71
## 131            snack products        27       0.07           98.78
## 132                       tea        27       0.07           98.85
## 133           potato products        23       0.06           98.91
## 134          abrasive cleaner        22       0.06           98.97
## 135                 nut snack        22       0.06           99.03
## 136           organic sausage        22       0.06           99.09
## 137                   tidbits        22       0.06           99.15
## 138              canned fruit        21       0.05           99.20
## 139                     syrup        21       0.05           99.25
## 140                 skin care        20       0.05           99.30
## 141                      soap        20       0.05           99.35
## 142                  prosecco        19       0.05           99.40
## 143          bathroom cleaner        17       0.04           99.44
## 144                  cookware        17       0.04           99.48
## 145            pudding powder        17       0.04           99.52
## 146              cocoa drinks        16       0.04           99.56
## 147    flower soil/fertilizer        16       0.04           99.60
## 148         cooking chocolate        15       0.04           99.64
## 149               ready soups        15       0.04           99.68
## 150                     honey        13       0.03           99.71
## 151                     cream        12       0.03           99.74
## 152             frozen fruits        11       0.03           99.77
## 153      specialty vegetables        11       0.03           99.80
## 154          organic products        10       0.03           99.83
## 155               decalcifier         9       0.02           99.85
## 156                hair spray         9       0.02           99.87
## 157                   liqueur         9       0.02           99.89
## 158                    whisky         8       0.02           99.91
## 159            salad dressing         6       0.02           99.93
## 160            frozen chicken         5       0.01           99.94
## 161           make up remover         5       0.01           99.95
## 162           rubbing alcohol         5       0.01           99.96
## 163            toilet cleaner         5       0.01           99.97
## 164                      bags         4       0.01           99.98
## 165            baby cosmetics         3       0.01           99.99
## 166           kitchen utensil         1       0.00           99.99
## 167     preservation products         1       0.00          100.00
## [1] "Variables processed: Member_number, itemDescription"
library(Hmisc)
Hmisc::describe(basket)
## basket 
## 
##  3  Variables      38765  Observations
## ---------------------------------------------------------------------------
## Member_number 
##        n  missing distinct 
##    38765        0     3898 
## 
## lowest : 1000 1001 1002 1003 1004, highest: 4996 4997 4998 4999 5000
## ---------------------------------------------------------------------------
## Date 
##        n  missing distinct 
##    38765        0      728 
## 
## lowest : 2014-01-01 2014-01-02 2014-01-03 2014-01-04 2014-01-05
## highest: 2015-12-26 2015-12-27 2015-12-28 2015-12-29 2015-12-30
## ---------------------------------------------------------------------------
## itemDescription 
##        n  missing distinct 
##    38765        0      167 
## 
## lowest : abrasive cleaner artif. sweetener baby cosmetics   bags             baking powder   
## highest: white bread      white wine       whole milk       yogurt           zwieback        
## ---------------------------------------------------------------------------

Filter and screen the dataframe

At this step it is importante to know the number of Members and the number of products.

library(magrittr)
# How many member
base::table(basket$Member_number) %>% length()
## [1] 3898
# 3898
# How many operations
length(basket$Member_number)
## [1] 38765
# 38765

# How many products
base::table(basket$itemDescription) %>% length()
## [1] 167
# 167

For all we have 3898 members and 167 products, and 38765 operations. This means that several members made several operations. How many operation per Members? And How many operations per product?

How many operations per Member

library(dplyr)
# How many transactions by Member, the data will be arranged by descending
basket %>% group_by(Member_number) %>% arrange(Member_number) %>% dplyr::summarise(N_operation=n()) %>% arrange(desc(N_operation))
#basket_plot_operations <- basket %>% group_by(Member_number, Date) %>% summarise(N_operation=n()) %>% arrange(desc(N_operation))

#ggplot2::ggplot(basket_plot_operations[1:100,], aes_string(x = 'Date', y = 'N_operation')) +
 # ggplot2::geom_bar(stat="identity", na.rm=TRUE)

This table confirm that the Member 3180 ahs the biggest frequency of operations 36. We can see the first ten important Members which got the biggest numbers of operations.

# How many Operations were done by product during 2 Years. The data will be arranged by descending
basket %>% group_by(itemDescription) %>% dplyr::summarise(N_operations=n()) %>% arrange(desc(N_operations))

This table shows arranges by descending the most important sold products.

We can visualize the first 50th best solds as following:

# How many transactions by product, the data will be arranged by descending
basket_plot_products <- basket %>% group_by(itemDescription) %>% dplyr::summarise(N_operations=n()) %>% arrange(desc(N_operations))


## plot the histogram of the best 50th sold  products
ggplot2::ggplot(basket_plot_products[1:50,], aes(x = reorder(itemDescription, -N_operations), y = N_operations)) +      
                                             #aes_string(x = 'itemDescription',  y = 'N_operations')  ## without ordering
 ggplot2::labs(title = "Overview of the first 50th best solds products during 2014-2015",
               #fill = "",
               x= "The products",
              #colour= Date,
               y = "The number of sales by product") +    
      ggplot2::theme(legend.title = element_text( colour="black",
                                                size=11,
                                                face="bold"),
                   title = element_text( size = 12,
                                         face = 'bold'
                   ),
                   text = element_text(size = 10,
                                       face= 'bold'
                   ),
                   axis.text.x=element_text(angle=45, hjust=1),
                   legend.position = "right",
                   legend.direction = "vertical"
    ) +
 ggplot2::geom_bar(stat="identity", na.rm=TRUE)

# Monitoring the operations number  were done per days, for all products during 2 years. The data will be arranged by descending
 basket_plot_date <-  basket %>% group_by(Date) %>% dplyr::summarise(N_operations=n()) # %>% arrange(desc(N_operations))
attach(basket_plot_date )
basket_plot_date %>%
ggplot(aes(x = Date, y = N_operations)) +
      geom_point(color = "darkorchid4") +
      geom_smooth(method = 'loess')+
      labs(title = "Total Operations per day during the all period (2 years)",
           subtitle = "Each value is the sum of all operations for all Members",
           y = "Number of Operations",
           x = "Date") + theme_bw(base_size = 15)

fit <- lm(N_operations~.,data= basket_plot_date)
plot(fit)

# library(tidyverse)
#  basket <- read.csv("basket_bkp.csv", header = TRUE, sep = ",")
# basket$X <- NULL
#  basket$Member_number <-as.factor(basket$Member_number)
# basket$Date <- as.Date(basket$Date, "%d-%m-%Y")
# 
# basket.new <- mutate(basket, variable = rownames(basket)) %>% 
#  tidyr::gather(basket, Date, itemDescription)

Regroupe all Operations by Month (December 2015)

## Determine the most 10 sold products
basket_products <- basket %>% group_by(itemDescription) %>% dplyr::summarise(N_operations=n()) %>% arrange(desc(N_operations))
basket_products10 <- as.data.frame(basket_products[1:10,])

basket %>% filter(itemDescription =="whole milk")
## Regroup all sold products in December 2015 (add index for each operation)
 #basket %>% #mutate(index = as.factor(seq.int(nrow(basket)))) %>%
 #mutate(Month = format(Date, "%B"), Year = format(Date, "%Y")) %>% arrange(desc(Date)) %>% filter(Month == "December", #Year == "2015") %>% dplyr::mutate(N = dplyr::summarise( n()))
  
 ## add a new column with Month_Year
 basket.Year_Month <- basket %>% mutate(Year_Month = substr(basket$Date, 1,7)) 
 
 # basket <- read.csv("basket_bkp.csv", header = TRUE, sep = ",")
 # basket$X <- NULL
 # basket %>% mutate(Member_number = as.factor(Member_number))
 # basket$Date <- as.Date(basket$Date, "%d-%m-%Y")
  
  #basket$Year_Month <- zoo::as.yearmon(basket$Year_Month)

basket.Year_Month%>% dplyr::group_by(Year_Month) %>%
  dplyr::summarise(N_Operations=n()) 
# Plot a subset of the data
#attach(Operations_Per_Month)
#ggplot(data =  Operations_Per_Month, aes_string(x = zoo::as.yearmon(Year_Month), y = N_operations)) + 
 # geom_line(color = "#FC4E07")

add index for each operation

basket %>% mutate(index = as.factor(seq.int(nrow(basket)))) 

Filter the 10 best sold products

basket_products <- basket %>% group_by(itemDescription) %>% dplyr::summarise(N_operations=n()) %>% arrange(desc(N_operations))
basket_products[1:10,]

Explore if all operations for each Member were done in the same day

The idea is to associate products per basket for each Member.

## group operations by Member and filter it by date
basket %>% group_by(Member_number) %>% arrange(Member_number) %>% filter(Date=="2015-05-27")

When We explore manually the table, we can see that some products sold together in the same date for the same Member. The response is: YES INITIATIVE TO PREDICT RULES BETWEEN PRODUCTS SOLD IN THE SAME TIME (BASKET: a group of products) IN SUPERMARKET FOR EXAMPLE.

combine all products per one Member

library(plyr)
## -------------------------------------------------------------------------
## You have loaded plyr after dplyr - this is likely to cause problems.
## If you need functions from both plyr and dplyr, please load plyr first, then dplyr:
## library(plyr); library(dplyr)
## -------------------------------------------------------------------------
## 
## Attaching package: 'plyr'
## The following object is masked from 'package:purrr':
## 
##     compact
## The following objects are masked from 'package:Hmisc':
## 
##     is.discrete, summarize
## The following objects are masked from 'package:dplyr':
## 
##     arrange, count, desc, failwith, id, mutate, rename, summarise,
##     summarize
#ddply(dataframe, variables_to_be_used_to_split_data_frame, function_to_be_applied)
transactionData_collapse_product <- plyr::ddply(basket,c("Member_number", "Date"),
                       function(basket)paste(basket$itemDescription,
                       collapse = ","))
transactionData_collapse_product
# remove Customer ID as we do not need it
transactionData_collapse_product$Member_number <- NULL
# remove Date as we do not need it
transactionData_collapse_product$Date <- NULL
colnames(transactionData_collapse_product) <- c("Products")
write.csv(transactionData_collapse_product, file = "transaction.csv", quote = FALSE, row.names = FALSE)
transactionData_collapse_product

Predict a rule between Product in each basket

Load transaction.csv to R, we will use read.transactions() function from Arules package this time.

library(arules)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following object is masked from 'package:tidyr':
## 
##     expand
## 
## Attaching package: 'arules'
## The following object is masked from 'package:dplyr':
## 
##     recode
## The following objects are masked from 'package:base':
## 
##     abbreviate, write
trans_basket <- read.transactions('transaction.csv', format = 'basket', sep=',')  #, rm.duplicates=TRUE
## Warning in asMethod(object): removing duplicated items in transactions
str(trans_basket)
## Formal class 'transactions' [package "arules"] with 3 slots
##   ..@ data       :Formal class 'ngCMatrix' [package "Matrix"] with 5 slots
##   .. .. ..@ i       : int [1:38007] 115 104 128 165 130 132 165 166 107 138 ...
##   .. .. ..@ p       : int [1:14965] 0 1 4 8 10 12 14 17 19 22 ...
##   .. .. ..@ Dim     : int [1:2] 168 14964
##   .. .. ..@ Dimnames:List of 2
##   .. .. .. ..$ : NULL
##   .. .. .. ..$ : NULL
##   .. .. ..@ factors : list()
##   ..@ itemInfo   :'data.frame':  168 obs. of  1 variable:
##   .. ..$ labels: chr [1:168] "abrasive cleaner" "artif. sweetener" "baby cosmetics" "bags" ...
##   ..@ itemsetInfo:'data.frame':  0 obs. of  0 variables
trans_basket
## transactions in sparse format with
##  14964 transactions (rows) and
##  168 items (columns)
summary(trans_basket) # call in summary to check our data
## transactions as itemMatrix in sparse format with
##  14964 rows (elements/itemsets/transactions) and
##  168 columns (items) and a density of 0.01511843 
## 
## most frequent items:
##       whole milk other vegetables       rolls/buns             soda 
##             2363             1827             1646             1453 
##           yogurt          (Other) 
##             1285            29433 
## 
## element (itemset/transaction) length distribution:
## sizes
##     1     2     3     4     5     6     7     8     9    10 
##   206 10012  2727  1273   338   179   113    96    19     1 
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    2.00    2.00    2.54    3.00   10.00 
## 
## includes extended item information - examples:
##             labels
## 1 abrasive cleaner
## 2 artif. sweetener
## 3   baby cosmetics

We can explore the data and make the frequency plot using the itemFrequencyPlot() function in the arules package. For this plot, we will check the top 10 products with absolute & relative frequency. The two plots give the same bihavior.

par(mfrow=c(1,2))
itemFrequencyPlot(trans_basket, topN=10, type='absolute', main="Absolute Product Frequency Plot")
itemFrequencyPlot(trans_basket, topN=10, type='relative', main="Relative Product Frequency Plot")

Modeling and Evaluation

We can start by mining the data for overall association rules.

Refering to our item frequency plots, let’s try to set minimum support at 1 in 1,000 operations and minimum confidence at 70 percent. Also we set the maximum number of Products to be associated as two

basket_rules <- arules::apriori(trans_basket, parameter = list(supp = 0.01, conf = 0.8))  #, maxlen=5
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport maxtime support minlen
##         0.8    0.1    1 none FALSE            TRUE       5    0.01      1
##  maxlen target   ext
##      10  rules FALSE
## 
## Algorithmic control:
##  filter tree heap memopt load sort verbose
##     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
## 
## Absolute minimum support count: 149 
## 
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[168 item(s), 14964 transaction(s)] done [0.00s].
## sorting and recoding items ... [64 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 done [0.00s].
## writing ... [0 rule(s)] done [0.00s].
## creating S4 object  ... done [0.00s].
rules <- sort(basket_rules, by='confidence', decreasing = TRUE)
summary(rules)
## set of 0 rules

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.